Kelowna, and to UBC's Okanagan campus. - CUMC - Canadian ...
Kelowna, and to UBC's Okanagan campus. - CUMC - Canadian ...
Kelowna, and to UBC's Okanagan campus. - CUMC - Canadian ...
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The <strong>Canadian</strong> Undergraduate<br />
Mathematics Conference<br />
2012<br />
Congrès Canadien des Étudiants en<br />
Mathématiques<br />
July 11-15 juillet 2012<br />
The University of British Columbia’s<br />
<strong>Okanagan</strong> Campus<br />
<strong>Kelowna</strong>, British Columbia
Contents<br />
1 Committee Notes 4<br />
1.1 Welcome / Bienvenue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4<br />
1.2 Welcome From Studc / Un message de Studc . . . . . . . . . . . . . . . . . . . . . . 5<br />
1.3 Committee Bios / Biographies des membres du comité . . . . . . . . . . . . . . . . . 7<br />
1.4 Attendee Policy / Politique de participation . . . . . . . . . . . . . . . . . . . . . . . 12<br />
2 Schedule of Events 14<br />
2.1 Basic Schedule / Horaire de base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14<br />
2.2 Comprehensive Schedule / Horaire de compléter . . . . . . . . . . . . . . . . . . . . 16<br />
2.3 Activities / Activités . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23<br />
3 Abstracts / Résumés 25<br />
3.1 Keynote Abstracts / Résumés plénière . . . . . . . . . . . . . . . . . . . . . . . . . . 25<br />
3.2 Student Abstracts / Résumés des étudiants . . . . . . . . . . . . . . . . . . . . . . . 28<br />
4 General Information / Informations générales 64<br />
4.1 Internet connections on <strong>campus</strong> / Connexions Internet sur les <strong>campus</strong> . . . . . . . . 64<br />
4.2 Getting <strong>to</strong>/from <strong>Okanagan</strong> College <strong>and</strong> the closing banquet . . . . . . . . . . . . . . 65<br />
4.3 <strong>Kelowna</strong> transit information / Le transport en commun á <strong>Kelowna</strong> . . . . . . . . . . 67<br />
4.4 Great places <strong>to</strong> eat in <strong>Kelowna</strong> / Bons endroits où manger à <strong>Kelowna</strong> . . . . . . . . 69<br />
4.5 Fun things <strong>to</strong> do in <strong>Kelowna</strong> / Activités amusantes à <strong>Kelowna</strong>: . . . . . . . . . . . . 70<br />
4.6 <strong>CUMC</strong> 2013 Host Bids / Enchères pour accueillir le CCÉM 2013 . . . . . . . . . . . 72<br />
4.7 Sponsors / Comm<strong>and</strong>itaires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74<br />
4.8 Riddles <strong>and</strong> Games / Énigmes et Jeux . . . . . . . . . . . . . . . . . . . . . . . . . . 78<br />
4.9 Campus Maps / Cartes du <strong>campus</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80<br />
3
Committee Notes<br />
1.1 Welcome / Bienvenue<br />
Welcome <strong>to</strong> the 19th annual <strong>Canadian</strong> Undergraduate Mathematics Conference! This year we are<br />
proud <strong>to</strong> present <strong>to</strong> you seven keynote speakers, in addition <strong>to</strong> the 86 student talks from over 25<br />
different universities <strong>and</strong> colleges from across Canada <strong>and</strong> the USA.<br />
UBC’s <strong>Okanagan</strong> <strong>campus</strong> aims <strong>to</strong> be ecologically friendly by focusing on sustainability through-<br />
out our <strong>campus</strong>. One of the ways we accomplish this is by being bottled water free; please<br />
make use of the reusable water bottles we have provided for you <strong>and</strong> the water stations in var-<br />
ious buildings. As well, please take note of the waste receptacles all around <strong>campus</strong> which are<br />
labelled for recyclable materials, returnable bottles, <strong>and</strong> other wastes. Please help keep our cam-<br />
pus <strong>and</strong> environment clean <strong>and</strong> healthy. For more information on our sustainability programs see<br />
www.ubc.ca/okanagan/sustainability.<br />
The <strong>CUMC</strong> is a unique opportunity for you <strong>to</strong> share ideas <strong>and</strong> make connections that could last<br />
you a lifetime. We know that you will be inspired by the talks you listen <strong>to</strong> <strong>and</strong> the people you<br />
meet this week. Enjoy your time here <strong>and</strong> welcome <strong>to</strong> beautiful <strong>Kelowna</strong>, BC!<br />
Bienvenue<br />
Bienvenue au 19e Concrès Canadien des Étudiants en Mathématiques! Cette année, nous sommes<br />
fiers de vous présenter sept conférences plénières, en plus des 86 présentations étudiantes de 25<br />
universités et collèges de par<strong>to</strong>ut au Canada et aux États-Unis.<br />
Le <strong>campus</strong> <strong>Okanagan</strong> de l’UBC a pour objectif d’être écologiquement responsable, en se con-<br />
centrant sur la durabilité à travers <strong>to</strong>ut le <strong>campus</strong>. L’une des façons d’accomplir cet objectif est de<br />
supprimer les bouteilles d’eau; nous vous prions donc de vous servir des bouteilles réutilisables que<br />
nous vous avons fournies, ainsi que des fontaines à eau disponibles dans plusieurs bâtiments. De<br />
plus, vous remarquerez que les poubelles sur le <strong>campus</strong> permettent le tri des matériaux recyclables,<br />
des bouteilles recyclables et des autres déchets. Nous vous serions gré de nous aider à garder notre<br />
4
1.2. WELCOME FROM STUDC / UN MESSAGE DE STUDC 5<br />
<strong>campus</strong> et notre environnement propres et sains. Pour plus d’informations sur notre programme de<br />
durabilité, vous pouvez visiter le www.ubc.ca/okanagan/sustainability.<br />
Le CCÉM est une opportunité unique de partager vos idées et de créer des relations qui pour-<br />
raient durer <strong>to</strong>ute votre vie. Nous savons que vous serez inspirés par les présentations que vous<br />
écouterez et par les personnes que vous rencontrerez. Nous vous souhai<strong>to</strong>ns un agréable séjour ici,<br />
et soyez les bienvenus au bel endroit qu’est <strong>Kelowna</strong>, en Colombie-Britannique!<br />
1.2 Welcome From Studc / Un message de Studc<br />
This year, the <strong>CUMC</strong> turns 19, the legal drinking age in British Columbia, <strong>and</strong> where better <strong>to</strong><br />
celebrate than in the heart of the province in the beautiful <strong>Okanagan</strong> Valley famous for its wineries.<br />
Much like any 19-year-old, the <strong>CUMC</strong> constantly changes: each year, participants <strong>and</strong> organizers<br />
bring the conference its unique flavour - from the crisp, sophisticated notes of Ontario <strong>to</strong> the bright,<br />
expressive aromas of Quebec <strong>to</strong> the mellow, luscious bouquet of the West coast. Throughout all this<br />
change <strong>and</strong> throughout all these years, what keeps the <strong>CUMC</strong> going is the enthusiasm of everyone<br />
involved. As the overseeing body, the CMS Student Committee (Studc) shares the excitement <strong>and</strong><br />
the passion of the organizers; we are happy <strong>to</strong> see the conference evolve - it supplies us with new<br />
ideas <strong>and</strong> influences our own projects. Studc not only ensures the continuation of the <strong>CUMC</strong>,<br />
it also supports regional events, publishes the semi-annual newsletter Notes from the Margin <strong>and</strong><br />
holds students events at the <strong>Canadian</strong> Mathematical Society’s winter <strong>and</strong> summer meetings. For<br />
more information on our past <strong>and</strong> present projects, check us out on the web at studc.cms.math.ca<br />
<strong>and</strong> don’t hesitate <strong>to</strong> drop us a line at chair-studc@cms.math.caas we are constantly looking for<br />
feedback.<br />
This year’s dynamic <strong>CUMC</strong> organizing team has done an amazing job putting <strong>to</strong>gether a great<br />
event. But it is the participants that make the conference happen, so we strongly encourage you <strong>to</strong><br />
partake in all of this year’s numerous activities. Whether on the wine <strong>to</strong>ur with <strong>Okanagan</strong>’s best<br />
or at breakfast with some OJ, I invite you <strong>to</strong> raise the glass in celebration of <strong>CUMC</strong> 2012.<br />
Un message de Studc<br />
Cette annèe, le CCÉM a enfin atteint l’âge légal pour boire en Colombie-Britannique et quoi de<br />
mieux que de célébrer cet événement au coeur de cette province, dans la magnifique vallée de<br />
l’<strong>Okanagan</strong> qui est reconnue pour ses vignobles. Á l’image des jeunes de 19 ans, le CCÉM est<br />
bouillonnant de projets. Chaque année, les participants et les organisateurs apportent leurs saveurs<br />
particuliéres, en commençant par les notes mordantes et sophistiquées de l’Ontario, aux arômes
6 CHAPTER 1. COMMITTEE NOTES<br />
expressifs et éclatants du Québec en passant par la tranquilité teintée d’extravagance de la côte<br />
Ouest canadienne.<br />
À travers le temps et les changements, ce qui tient en vie le CCÉM est certainement l’enthousiasme<br />
de <strong>to</strong>utes les personnes impliquées dans levènement. En tant qu’organisation chapeautant le congrès,<br />
le comité étudiant de la SMC (Studc) partage l’effervessence et la passion des organisateurs. Nous<br />
sommes heureux de constater que le congrès évolue, nous amenant de nouvelles idées et influenant<br />
nos projets. En plus d’assurer la continuité du CCÉM, le Studc supporte des événements régionaux,<br />
publie deux fois par année le bulletin “Notes from the Margin” et organise des activités étudiantes<br />
aux deux rencontres annuelles de la Société Mathématique du Canada. Pour plus d’informations<br />
sur nos projets passés et actuels, allez visiter notre site web studc.cms.math.ca et n’hésitez pas á<br />
nous écrire à chair-studc@cms.math.ca. Nous sommes <strong>to</strong>ujours ouverts aux commentaires.<br />
Le dynamique comité organisateur de cette année a mis beaucoup d’efforts dans l’organisation<br />
de ce congrès. Par contre, ce sont les participants qui font en sorte que le congrès est possible et<br />
c’est pourquoi nous vous encourageons fortement à participer aux nombreuses activités qui s’offrent<br />
à vous cette année. Que ce soit pendant la <strong>to</strong>urnée des vignobles de la vallée de l’<strong>Okanagan</strong> ou en<br />
savourant un bon jus d’orange frais au déjeuner, vous êtes invités à lever votre verre pour célébrer<br />
le CCÉM 2012.
1.3. COMMITTEE BIOS / BIOGRAPHIES DES MEMBRES DU COMITÉ 7<br />
1.3 Committee Bios / Biographies des membres du comité<br />
Figure 1.1: Committee from left <strong>to</strong> right: Crystal Parras, Jodie Foster, Spencer Hunt, Garrett<br />
Culos, Andrea Hyde, Rodney Earl <strong>and</strong> Faisal Rahman.<br />
Crystal Parras - President<br />
Crystal Parras is going in<strong>to</strong> her fourth year of BSc Applied Math with Honours at UBC’s<br />
<strong>Okanagan</strong> <strong>campus</strong>. Having first been a hairdresser for ten years, she <strong>to</strong>ok a turn in<strong>to</strong> a completely<br />
different direction <strong>and</strong> now uses pencils <strong>and</strong> graph paper as her weapon of choice instead of scissors...<br />
though who’s <strong>to</strong> say what would cause more damage! She is looking forward <strong>to</strong> delving in<strong>to</strong> courses<br />
on financial math <strong>and</strong> statistics in the fall, <strong>and</strong> her goal is <strong>to</strong> continue this on in<strong>to</strong> graduate studies.<br />
Crystal is also President of the Math <strong>and</strong> Stats Course Union, <strong>and</strong> when she’s not studying, you<br />
can catch her snowboarding, dancing around <strong>to</strong> drum ‘n’ bass, cutting her friends’ hair, <strong>and</strong> just<br />
being a general nuisance.<br />
Crystal Parras débute sa quatrième anne d’étude au Baccalauréat en Mathématiques Appliquées<br />
à l’UBCO. Après avoir travaillé comme coiffeuse durant 10 ans, elle a emprunt une <strong>to</strong>ute autre<br />
direction et a troqué ses ciseaux pour des crayons et du papier quadrillé. Dans les prochaines<br />
années elle envisage de s’orienter vers les statistiques et les mathématiques financières dans le but<br />
de poursuivre des études supérieures. Crystal est aussi Présidente du Math <strong>and</strong> Stats Course Union<br />
et lorsqu’elle n’étudie pas, elle aime faire de la planche à neige, danser au son du drum n bass et<br />
couper les cheveux de ses amis.
8 CHAPTER 1. COMMITTEE NOTES<br />
Andrea Hyde - VP Logistics<br />
Andrea Hyde completed her BSc in Math with Honours at UBCO this year. Her undergraduate<br />
work was in Mathematical Biology under the supervision of Dr. Rebecca Tyson. She is excited <strong>to</strong><br />
begin her MSc this fall in Number Theory with Dr. Blair Spearman at UBCO. Andrea is also the<br />
Internal Co-ordina<strong>to</strong>r for the Math <strong>and</strong> Stats Course Union on <strong>campus</strong>. When not being a terrible<br />
nerd, Andrea loves biking, snowboarding, drinking beer with friends, <strong>and</strong> cuddling with her dogs.<br />
She highly recommends that you have the all you can eat waffles at the Jammery while you’re here.<br />
Andrea Hyde vient <strong>to</strong>ut juste de compléter son baccalauréat en mathématiques à l’UBCO. Son<br />
projet d’étude a porté sur la biologie mathématique, sous la supervision de Rebecca Tyson. Elle<br />
est enthousiaste à l’idée de commencer sa maîtrise à àu<strong>to</strong>mne dans le domaine de la théorie des<br />
nombres avec Blair Spearman à UBCO. En plus de son implication pour le CCÉM, Andrea est<br />
Coordinatrice Interne du Math <strong>and</strong> Stats Course Union. À part être une incroyable ’nerd’, Andrea<br />
aime faire du vélo, de la planche à neige, boire de la bière avec des amis et jouer avec ses chiens.<br />
Selon elle, un déjeuner au crêpes-à-volonté du Jammery s’impose lors de votre passage à <strong>Kelowna</strong>.<br />
Spencer Hunt - VP Finance<br />
Spencer has grown up in the <strong>Okanagan</strong> in the small <strong>to</strong>wn of <strong>Okanagan</strong> Falls (there wasn’t even<br />
a Tim Hor<strong>to</strong>ns!). Throughout his four years at UBC’s <strong>Okanagan</strong> <strong>campus</strong>, Spencer has tried <strong>to</strong> be<br />
involved with the <strong>campus</strong> community. Working on <strong>campus</strong> as a residence advisor, teaching assistant,<br />
supplemental learning leader, <strong>and</strong> as the orientation coordina<strong>to</strong>r, has fueled his passion for students<br />
<strong>and</strong> helping them succeed. Spencer was also a part of the President’s non-academic misconduct<br />
committee, where the students would serve as an impartial body <strong>to</strong> students that have broken the<br />
<strong>campus</strong> conduct. Being a part of this committee has encouraged him <strong>to</strong> attend law school, <strong>and</strong><br />
he will be taking the LSAT later this year. Spencer feels that his education in mathematics will<br />
provide him the objectivity <strong>and</strong> analytical skills <strong>to</strong> succeed on this career path.<br />
Spencer Hunt a gr<strong>and</strong>i dans le petit village d’<strong>Okanagan</strong> Falls (où il n’y a même pas de Tim Hor-<br />
<strong>to</strong>ns!). Pendant ses quatres années sur le <strong>campus</strong> de UBCO, Spencer s’est impliqué de nombreuses<br />
faons. Il a travaillé à titre de responsable de résidences, d’auxiliaire d’enseignement et de conseiller<br />
en orientation, ce qui a alimenté sa passion pour la réussite des étudiants. Spencer a également<br />
fait partie du President non-academic misconduct committee, dans lequel les étudiants servent de<br />
corps impartial dans le jugement des étudiants ayant enfreint les lois du <strong>campus</strong>. Prendre part à<br />
ce comité l’a encouragé à s’inscrire à l’école de droit et il passera ses examens d’admission dans le<br />
courant de l’année. Spencer considre que ses études en mathématiques lui ont donné l’objectivité<br />
et les outils analytiques nécessaires pour réussir dans sa future carrière.
1.3. COMMITTEE BIOS / BIOGRAPHIES DES MEMBRES DU COMITÉ 9<br />
Rodney Earl - VP Logistics<br />
Rodney Earl is going in<strong>to</strong> his fifth year of his BSc with a double major, one in Computer Science<br />
<strong>and</strong> the other in Mathematics, with a concentration in Pure Math. Math has always been a hobby<br />
of Rodney’s <strong>and</strong> became more of a passion as he continued his years of study. By the end of his<br />
second year, he knew that underst<strong>and</strong>ing how <strong>and</strong> why math works was very interesting <strong>to</strong> him, so<br />
he decided <strong>to</strong> take a concentration in the pure side of math. Outside of school, Rodney is a member<br />
of the Cadet Instruc<strong>to</strong>r Cadre, which is a sub component of the <strong>Canadian</strong> Forces, that specializes in<br />
the instruction, men<strong>to</strong>ring <strong>and</strong> development of youth in the Cadet Program. When not studying,<br />
working on projects or planning different activities for Cadets, Rodney enjoys reading <strong>and</strong> hanging<br />
out with his friends.<br />
Rodney Earl débute sa cinquième année de baccalauréat avec majeure double en Informatique<br />
et en Mathématiques. Les mathématiques ont <strong>to</strong>ujoursété un passe-temps pour Rodney et sont<br />
devenues une passion au cours de ses études. À la fin de sa deuxième année, il savait que la<br />
compéhension du fonctionnement des mathématiques était de première importance pour lui, ce qui<br />
l’a mené vers les mathématiques pures. En dehors du cadre scolaire, Rodney est un membre des<br />
Cadres Instructeurs des Cadets, une organisation affiliée aux Forces Canadiennes qui se spécialise<br />
dans la formation et le développement des jeunes Cadets. Dans ses temps libres, Rodney aime lire<br />
et passer du bon temps avec ses amis.<br />
Jodie Foster - VP Fundraising<br />
Jodie is entering her final year of a BSc in Mathematical Sciences with a minor in Physics. She<br />
is greatly looking forward <strong>to</strong> an awesome last year with her involvement as a teaching assistant in<br />
Math <strong>and</strong> Statistics as well as her position as the student coordina<strong>to</strong>r for the Math <strong>and</strong> Science<br />
Tu<strong>to</strong>r Centre. Next year she will be starting her MSc in Astrostatistics. In her spare time Jodie<br />
can be found travelling the world. She has spent time in both Sweden <strong>and</strong> Bolivia. Jodie also likes<br />
<strong>to</strong> spend her time in the <strong>Okanagan</strong> with friends <strong>and</strong> family. Fun fact: Jodie’s obsessive love for<br />
Harry Potter <strong>and</strong> Star Wars (she owns 12 bobble heads of various characters) has provided her the<br />
attainment of badass status.<br />
Jodie débute sa dernière année de baccalauréat en mathématiques avec mineure en physique.<br />
Elle envisage une superbe année compte tenu de son implication comme auxiliaire d’enseignement<br />
et comme coordonnatrice étudiante du centre de tu<strong>to</strong>rat. Par la suite, elle compte faire une maîtrise<br />
en Astrophysiques. Dans ses temps libres, Jodie aime passer du temps dans la vallée de l’<strong>Okanagan</strong><br />
avec sa famille et ses amis. Fait cocasse: L’obsession de Jodie pour Harry Potter et Star Wars
10 CHAPTER 1. COMMITTEE NOTES<br />
(elle possède 12 bobble heads de diffrents personnages) est la seule chose qui l’empêche d’obtenir le<br />
statut de “badass”.<br />
Faisal Rahman - Web Coordina<strong>to</strong>r<br />
Faisal Rahman started his academic career with an obsession for Machine Learning <strong>and</strong> Artificial<br />
Intelligence, but slowly his passion grew for Mathematics. He feels blessed <strong>to</strong> be able <strong>to</strong> see the<br />
beauty of Mathematics behind equations. While he has his weakness for theoretical mathematics,<br />
he also allows himself <strong>to</strong> explore his affection for other branches of arts <strong>and</strong> science. His career<br />
dream is <strong>to</strong> aid the study of human behavior with mathematics, <strong>and</strong> possibly extend the research<br />
<strong>to</strong> Artificial Intelligence. He enjoys dancing, sports, <strong>and</strong> looking at paintings. He gets inspired by<br />
the success of others, <strong>and</strong> always inspires others <strong>to</strong> reach their potential. His true inspiration is<br />
Salman Khan, who in his graduation speech said, “It is no exaggeration <strong>to</strong> say that we will change<br />
the world”, <strong>and</strong> later formed the Khan Academy, which helps educate millions of people.<br />
Faisal Rahman a dèbuté sa carrière académique avec une obsession pour l’intelligence artifielle et<br />
l’apprentissage au<strong>to</strong>matique, puis sa passion pour les mathématiques s’est graduellement dévelop-<br />
pée. Il se considère chanceux de saisir la beauté des mathématiques au-delà des équations. Même<br />
si les mathématiques théoriques le captivent, il aime explorer d’autres branches des arts et des<br />
sciences. Dans sa future carrière, il voudrait étudier le comportement humain grâce aux mathéma-<br />
tiques et peut-être même poursuivre ses recherches dans le domaine de l’intelligence artificielle. Il<br />
aime la danse, les sports et les peintures. Il est inspiré par le succès de ses collègues et inspire les<br />
autres à atteindre leur plein potentiel. Il puise son inspiration dans Salman Khan, qui a dit dans<br />
son discours de graduation que “ce n’est pas de l’exagération de dire que l’on va changer le monde”<br />
et qui a fondéla Khan Academy, qui aide à éduquer des millions de personnes.<br />
Garrett Culos - VP Fundraising<br />
Garrett Culos is going in<strong>to</strong> his fifth <strong>and</strong> final year at UBC’s <strong>Okanagan</strong>, where he is studying<br />
applied math <strong>and</strong> physics. He will be ending his undergraduate degree by undertaking two honours<br />
projects specializing in mathematical biology <strong>and</strong> theoretical physics. When Garrett is not studying,<br />
he enjoys going <strong>to</strong> the gym where he picks things up <strong>and</strong> puts them down. Garrett is a tall man,<br />
who finds pleasure in playing video games such as Starcraft, Diablo, <strong>and</strong> Fallout 3. Garrett also<br />
enjoys long walks on the beach, going <strong>to</strong> the park <strong>to</strong> do acrobatic yoga, <strong>and</strong> talking in the third<br />
person. If there’s one thing that Garrett stresses most about <strong>Kelowna</strong> is <strong>to</strong> bask in the glory that<br />
is the Wood Fire Bakery <strong>and</strong> enjoy their succulent chicken cordon bleu.<br />
Garrett Culos amorce sa cinquième et dernière annèe á l’UBCO où il étudie les mathématiques<br />
et la physique appliquées. Il terminera ses études de premier cycle avec deux projets d’envergure
1.3. COMMITTEE BIOS / BIOGRAPHIES DES MEMBRES DU COMITÉ 11<br />
en biologie mathématique et en physique théorique. Mis à part l’école, Garrett aime s’entraîner au<br />
gym où il lève de la fonte. Garrett aime aussi jouer à des jeux tels que Starcraft, Diablo et Fallout<br />
3. Il aime aussi les longues marches sur la plage, aller au parc faire du yoga acrobatique et parler<br />
à la troisième personne. S’il pouvait insister sur une chose à faire à <strong>Kelowna</strong>, ce serait de profiter<br />
du temps au Wood Fire Bakery en savourant leur poulet cordon bleu.
12 CHAPTER 1. COMMITTEE NOTES<br />
1.4 Attendee Policy / Politique de participation<br />
The <strong>Canadian</strong> Undergraduate Mathematics Conference 2012 is dedicated <strong>to</strong> providing a harassment-<br />
free conference experience for everyone, regardless of gender, sexual orientation, disability, physical<br />
appearance, body size, race, religion, language, or mathematical preference. We do not <strong>to</strong>lerate<br />
harassment of conference participants in any form. Sexual language <strong>and</strong> imagery is not appropriate<br />
for any conference venue, including talks. Conference participants violating these rules may be<br />
sanctioned or expelled from the conference without a refund at the discretion of the conference<br />
organizers.<br />
Harassment includes: offensive verbal comments related <strong>to</strong> gender, sexual orientation, disability,<br />
physical appearance, body size, race, or religion; sexual images in public spaces; following, stalking,<br />
deliberate intimidation, unwelcome pho<strong>to</strong>graphy or recording; sustained disruption of talks or other<br />
events; <strong>and</strong> inappropriate physical contact, or unwelcome sexual attention. Participants asked <strong>to</strong><br />
s<strong>to</strong>p any harassing behavior are expected <strong>to</strong> comply immediately.<br />
If a participant engages in harassing behavior, the conference organizers may take any action<br />
they deem appropriate, including issuing a warning or removing the offender from the conference<br />
with no refund. If you are being harassed, notice that someone else is being harassed, or have any<br />
other concerns, please contact a member of conference staff immediately. Conference staff can be<br />
identified by coloured Organizer <strong>and</strong> Volunteer t-shirts.<br />
Conference staff will be happy <strong>to</strong> help participants contact <strong>campus</strong> security or local law en-<br />
forcement, or otherwise assist those experiencing harassment <strong>to</strong> feel safe for the duration of the<br />
conference. Campus security can provide escorts if desired. We value your attendance.<br />
If you have any questions regarding the policy or its enforcement, please don’t hesitate <strong>to</strong> contact<br />
us at the email below.<br />
<strong>CUMC</strong> 2012 Organizing Committee E-mail: cumc.2012@ubc.ca<br />
Campus Security (Emergency): 250-807-8111<br />
Campus Security (Non-Emergency): 250-807-9236<br />
On-Campus Accommodation: 250-807-8050<br />
Police/Fire/Ambulance (Emergency): 911<br />
RCMP (Non-Emergency): 250-726-3300<br />
Taxi: 250-861-1111 or 250-212-1212<br />
<strong>Kelowna</strong> Crisis Line: 1-888-353-2273<br />
<strong>Okanagan</strong> College Security (Non-Emergency): 250-317-2435
1.4. ATTENDEE POLICY / POLITIQUE DE PARTICIPATION 13<br />
Politique de participation<br />
Le Congrès Canadien des Étudiants en Mathématiques 2012 s’engage à fournir une expérience de<br />
congrès exempte de harcèlement pour <strong>to</strong>us, quels que soient le genre, l’orientation sexuelle, les<br />
invalidités, l’apparence physique, la taille, la race, la religion, la langue ou les préférences mathé-<br />
matiques de la personne. Nous ne <strong>to</strong>lérerons le harcèlement de participants au congrès d’aucune<br />
forme. Le langage et les images à caractère sexuel ne sont appropriées ni lors des conférences ni<br />
lors des présentations. Les participants aux conférences contrevenant á ces règles pourront être<br />
sanctionnés ou expulsés des conférences sans remboursement, à la discrétion des organisateurs.<br />
Le harcèlement inclut : les commentaires verbaux offensifs liés au genre, à l’orientation sex-<br />
uelle, aux invalidités, à l’apparence physique, à la taille, à la race, à la religion, à la langue ou<br />
aux préférences mathématiques; l’affichage d’images sexuels dans les espaces publics; le harcèle-<br />
ment criminel, la traque, l’intimidation délibérée, les pho<strong>to</strong>graphies ou enregistrements déplacés;<br />
des interruptions soutenues de présentations ou d’autres événements et des contacts physiques in-<br />
appropriés ou une attention sexuelle importune. Les participants à qui l’on dem<strong>and</strong>era d’arrêter<br />
<strong>to</strong>ut comportement d’harcèlement devront se conformer aux dem<strong>and</strong>es immédiatement.<br />
Si un participant se livre à un comportement de harcèlement, les organisateurs des conférences<br />
pourront prendre <strong>to</strong>utes les mesures qu’ils jugeront appropriées, y compris émettre un avertissement<br />
ou retirer le délinquant du congrès sans remboursement. Si vous êtes harcelés, remarquez que<br />
quelqu’un est harcelé, ou avez connaissance de <strong>to</strong>ut autre renseignement pertinent, nous vous serions<br />
gré de contacter un membre du personnel (organisateurs ou bénévoles) immédiatement. Ils peuvent<br />
être repérés grâces aux t-shirts colorés.<br />
Les membres du personnel seront heureux dider les participants à contacter la sécurité du<br />
<strong>campus</strong>, ou le bureau de loi local, ou dider ceux qui subissent le harcèlement à se sentir en sécurité<br />
pour <strong>to</strong>ute la durée du congrès. La sécurité du <strong>campus</strong> peut aussi fournir des escortes si nécessaire.<br />
Nous tenons à votre présence et à votre sécurité.<br />
Pour <strong>to</strong>ute question concernant la politique ou son application, n’hésitez pas à nous contacterà<br />
l’adresse de courriel électronique ci-dessous.<br />
Comité d’organisation du CCÉM: cumc.2012@ubc.ca<br />
Sécurité du Campus (Urgences): 250-807-8111<br />
Sécurité du Campus : 250-807-9236<br />
Hébergment sur le Campus: 250-807-8050<br />
Police/Pompiers/Ambulance (Urgences): 911<br />
GRC (Sans urgence): 250-726-3300<br />
Taxi: 250-861-1111 or 250-212-1212<br />
Ligne de crise de <strong>Kelowna</strong>: 1-888-353-2273<br />
Sècurité du College <strong>Okanagan</strong> (Sans urgence): 250-317-2435
Schedule of Events<br />
2.1 Basic Schedule / Horaire de base<br />
Wednesday July 11, 2012 - Mercredi 11 juillet<br />
13:00 Check in / Enregistrement<br />
15:30 Refreshments / Pause café<br />
16:00 Opening Remarks / Discours d’ouverture<br />
17:00 Keynote Speaker / Conférence plénière - Tim Swartz<br />
18:30 Opening Banquet / Banquet d’ouverture<br />
Thursday July 12, 2012 - Jeudi 12 juillet<br />
9:00 Student Talks / Conférences étudiantes<br />
11:00 Coffee Break / Pause café<br />
11:30 Keynote Speaker / Conférence plénière - Heinz Bauschke<br />
12:30 Lunch / Dîner<br />
14:00 Student Talks / Conférence étudiantes<br />
15:00 Coffee Break / Pause café<br />
15:30 Keynote Speaker / Conférence plénière - Donovan Hare<br />
17:00 Wine Tour (Optional Activity) / Tournée vinicole (Activité facultative) (section 2.3)<br />
20:00 Movie Night (Optional Activity) / Soirée cinéma (Activité facultative) (section 2.3)<br />
Friday July 13, 2012 - Vendredi 13 juillet<br />
7:45 Buses <strong>to</strong> <strong>Okanagan</strong> College / Transport vers <strong>Okanagan</strong> College (see section 4.2)<br />
8:50 Opening Remarks from <strong>Okanagan</strong> College / Discours d’ouverture du <strong>Okanagan</strong> College<br />
9:00 Student Talks / Conférence étudiantes<br />
11:00 Coffee Break / Pause café<br />
11:30 Keynote Speaker / Conférence plénière - Jennifer Hyndman<br />
14
2.1. BASIC SCHEDULE / HORAIRE DE BASE 15<br />
12:30 Lunch / Dîner<br />
14:00 Student Talks / Conférence étudiantes<br />
16:00 Coffee Break / Pause café<br />
16:30 Keynote Speaker / Conférence plénière - Catherine Beauchemin<br />
17:30 <strong>CUMC</strong> 2013 Host Bids / Enchères pour accueillir le CCÉM 2013 ( section 4.6)<br />
18:30 Women in Math <strong>and</strong> Science Dinner (Optional Activity) / Souper pour les Femmes en Maths<br />
et Sciences (Activité facultative)(see section 2.3)<br />
18:30 Sc<strong>and</strong>ia (Optional Activity)/(Activité facultative)(see section 2.3).<br />
Saturday July 14, 2012 - Samedi 14 juillet<br />
9:00 Student Talks / Conférence étudiantes<br />
11:00 Coffee Break / Pause café<br />
11:30 Keynote Speaker / Conférence plénière - Dominikus Noll<br />
12:30 Lunch / Dîner<br />
14:00 Student Talks / Conférence étudiantes<br />
15:00 Coffee Break / Pause café<br />
15:30 Keynote Speaker / Conférence plénière - Gerda de Vries<br />
17:30 Closing Banquet / Banquet final<br />
19:45 Announcement of <strong>CUMC</strong> 2013 Host University / L’annonce de l’université d’accueil CCÉM<br />
2013<br />
Sunday July 15, 2012 - Dimanche 15 Juillet<br />
Free day <strong>to</strong> <strong>to</strong>ur <strong>Kelowna</strong>/ Journée libre pour visiter <strong>Kelowna</strong>
16 CHAPTER 2. SCHEDULE OF EVENTS<br />
2.2 Comprehensive Schedule / Horaire de compléter<br />
Wednesday July 11, 2012 - Mercredi 11 juillet<br />
Time - Heure Description Room - Local<br />
13:00 - 15:30 Check in / Enregistrement Fipke Foyer<br />
15:30 - 16:00 Refreshments / Pause café Fipke Foyer<br />
16:00 - 16:20 Opening Remarks / Discours d’ouverture Fip 204<br />
16:20 - 17:00 Carolyn Labun - How <strong>to</strong> Make Your Conference Presentation<br />
Count<br />
17:00 - 18:00 Keynote Speaker / Conférence plénière : Tim Swartz -<br />
Statistical Excursions in Sport<br />
Fip 204<br />
Fip 204<br />
18:30 - 20:30 Opening Banquet / Banquet d’ouverture The Commons<br />
Thursday July 12, 2012 - Jeudi le 12 juillet<br />
(behind the<br />
UNC)<br />
Time - Heure Description Room - Local<br />
9:00 - 10:00<br />
10:00 - 10:30<br />
Ruth, William - Introduction <strong>to</strong> Estimation Fipke 124<br />
Simard, Nicolas - Euclid‘s Elements <strong>and</strong> Pythagoras’ Theorem Fipke 138<br />
Baker, Michael - Special Functions <strong>and</strong> Orthoganal Polynomials Fipke 121<br />
Tawfik, Selim - Parallel Parking with Lie Algebras Fipke 140<br />
Raymond-Beizile, Léo - Causal inference <strong>and</strong> Bayesian propensity<br />
score adjustment methods<br />
Fipke 250<br />
Marceau, Jean-François - Introduction <strong>to</strong> Additive Frieze Patterns Fipke 129<br />
Hyde, Andrea - An Individual Based Model for Bear Movement Fipke 124<br />
Poelstra, Andrew - On the Existence of Double Arithmetic Pro-<br />
gressions<br />
Fipke 138<br />
Beckett, Mathew - Scaling Arguments on the Space of Connections Fipke 121<br />
Mehta, Arthur - The S<strong>to</strong>ry of Srinivasa Ramanujan Fipke 140<br />
Godin, Jonathan - Analysis Around Fractals Fipke 250<br />
Luther, Robert - Combina<strong>to</strong>rial Designs <strong>and</strong> Block-Intersection<br />
Graphs<br />
Fipke 129
2.2. COMPREHENSIVE SCHEDULE / HORAIRE DE COMPLÉTER 17<br />
10:30 - 11:00<br />
Banero, Graham - Abelian <strong>and</strong> Additive Complexity: Analyzing<br />
Structure in Infinite Words<br />
Foster, Jodie - Supplemental Learning: A New Way <strong>to</strong> Learn<br />
Mathematics!<br />
Fipke 124<br />
Fipke 138<br />
Richards, Larissa - Pattern Subgroups of GLn(F) Fipke 121<br />
Ryan, Philip - As Easy as A, B, C Fipke 140<br />
Deschênes, Andréa - Connexions et Calcul Rigourex Fipke 250<br />
Recoskie, Jeremy - Critical Issues in Statistical <strong>and</strong> Biological In-<br />
terperetation<br />
Fipke 129<br />
11:00 - 11:30 Coffee Break / Pause café Fipke Foyer<br />
11:30 - 12:30 Keynote Speaker / Conférence plénière: Heinz Bauschke<br />
- An invitation <strong>to</strong> projection methods<br />
Fip 204<br />
12:30 - 13:30 Lunch / Dîner Fipke Foyer<br />
14:00 - 15:00<br />
Pynn-Coates, Nigel - VC Dimension <strong>and</strong> Density: Connections<br />
between Computational Learning Theory <strong>and</strong> Model Theory<br />
Hsu, Chieh-Ting (Jimmy) - The Convergence Criterias of the<br />
Bayesian Monte Carlo Simulation on the Quantification of the<br />
Number of Fluorophores in a Cell<br />
Charlesworth, Ian - DFAs, Au<strong>to</strong>matic Numbers, <strong>and</strong> Transcen-<br />
dence<br />
Tarzwell, Caleb - Modelling Techniques of Genetic Information<br />
Flow: Past <strong>and</strong> Future<br />
Fipke 124<br />
Fipke 138<br />
Fipke 121<br />
Fipke 140<br />
Snarski, Michael - Representations of Harmonic Donuts Fipke 250<br />
Asad, Reza - Steiner Symmetrizations: Convergence <strong>and</strong> Rate of<br />
Convergence<br />
Fipke 129<br />
15:00 - 15:30 Coffee Break / Pause café Fipke Foyer<br />
15:30 - 16:30 Keynote Speaker / Conférence plénière: Donovan Hare -<br />
To All the Graphs I’ve Loved Before<br />
17 :00 - 20:30 Wine Tour (Optional Activity) / Tournée vinicole (Activité fac-<br />
ultative) (section 2.3)<br />
20 :00 - 22:00 Movie Night (Optional Activity) / Soirée cinéma (Activité facul-<br />
tative) (section 2.3)<br />
Fip 204<br />
Meet at UBC-O<br />
bus loop<br />
UNC movie the-<br />
atre
18 CHAPTER 2. SCHEDULE OF EVENTS<br />
Friday July 13, 2012 - Vendredi 13 juillet<br />
Time - Heure Description Room - Local<br />
8:50-9:00 Opening Remarks from <strong>Okanagan</strong> College / Discours d’ouverture<br />
9:00 - 10:00<br />
10:00 - 10:30<br />
10:30 - 11:00<br />
du <strong>Okanagan</strong> College<br />
Papst, Irena - From Differential Equations <strong>to</strong> Diphtheria: The<br />
Mathematics of Infectious Disease Spread<br />
C<strong>and</strong>ales, Manuel - Cyclo<strong>to</strong>mic Polynomials <strong>and</strong> Elementary<br />
Number Theory<br />
Centre for<br />
Learning Atrium<br />
E202<br />
E207<br />
Charron, Philippe - Temperley Lieb Algebras E103<br />
Pelletier, Laurent - Probability <strong>and</strong> Measure E208<br />
Szatmari, Simon - Lie Group Methods for Moving Mesh Algo-<br />
rithms<br />
Klusowski, Jason - Flows, Branching Numbers, <strong>and</strong> Percolation<br />
on Trees<br />
E212<br />
E213<br />
Parras, Crystal - A Brief His<strong>to</strong>ry of Women in Mathematics E202<br />
Reimer, Sarah - Lost in Inversion: Conditioning of Spectral Col-<br />
location Methods<br />
Horan, Joseph - Qualitative Analysis of Chemical Reaction Net-<br />
works<br />
E207<br />
E103<br />
Wu, Steven - A Winning Strategy E208<br />
Tavakoli, Arman - Introducing Uniformly Distributed sequences E213<br />
Leylan, Richard - The Roots of Flow <strong>and</strong> Chromatic Polynomials E202<br />
Hunt, Spencer - Derivative Free Optimization Techniques on a<br />
series of test functions<br />
Hunt, Sean - Cooking Howard’s Curry With The Agda Program-<br />
ming Language<br />
E207<br />
E103<br />
Maheux, Dominique - Introduction aux Méthodes de Schwarz E208<br />
Dranovski, Anne - Rate of Convergence of R<strong>and</strong>om Polarizations E213<br />
11:00 - 11:30 Coffee Break / Pause café Centre for<br />
Learning Atrium
2.2. COMPREHENSIVE SCHEDULE / HORAIRE DE COMPLÉTER 19<br />
11:30 - 12:30 Keynote Speaker / Conférence plénière: Jennifer Hynd-<br />
man - Finite Bases of Quasi-equations of Unary Algebras: How<br />
Few Rules Can We Get Away With?<br />
Centre for<br />
Learning Atrium<br />
12:30 - 14:00 Lunch / Dîner Centre for<br />
14:00 - 14:30<br />
14:30 - 15:00<br />
15:00 - 15:30<br />
Lévesque, Jean-Sébastien - Brain, Dynamical Systems <strong>and</strong> Fun! E202<br />
Street, Colin - Intuition <strong>and</strong> Probability E207<br />
Bouchard, Nicolas - Calcul formel et programmation / Program-<br />
ming computer algebra<br />
Learning Atrium<br />
E103<br />
Gerbelli-Gauthier, Mathilde - Introduction <strong>to</strong> Modular Forms E208<br />
Zung, Jonathan - How Topologically Inclined Thieves Split Their<br />
Spoils<br />
E212<br />
Tufts, Julia - Domination Polynomials of Graphs <strong>and</strong> Their Roots E213<br />
Jackett, Neal - An Introduction <strong>to</strong> Topology E202<br />
Funk, Jacob - Stabilization Time for a Type of Evolution on Bi-<br />
nary Strings<br />
E207<br />
Gervais, Kevin - Introduction à l’Homologie Singuliére E103<br />
Klassen, Jamie - Representations <strong>and</strong> Duality with a View To-<br />
wards Number Theory<br />
E208<br />
Petrie, Tara - Math <strong>and</strong> Art: the Math Behind the Beauty E212<br />
Josh Holt, Richard Hudson, Bryan Zintel - Exponential Model of<br />
the Eiffel Tower<br />
Culos, Garrett - Predicting the Spatial Distribution of an Orchard<br />
Insect Pest<br />
Beg, Nikolina - Principal Component Analysis <strong>and</strong> its Application<br />
<strong>to</strong> High Dimensional Data Sets<br />
E213<br />
E202<br />
E207<br />
Kabir, Ifaz - A Simple proof of the Jordan Curve Theorem E103<br />
Sequeira, Nigel - Continuous Model Theory <strong>and</strong> Von Neumann<br />
Algebras<br />
E208<br />
Provost, Alex - A Topological Proof of the Infinitude of Primes E212<br />
Al-Shaghay, Abdullah - An Irreducibility Criterion of A. Cohn E213
20 CHAPTER 2. SCHEDULE OF EVENTS<br />
15:30 - 16:00<br />
Bidart, Rene - What is Underst<strong>and</strong>ing? E202<br />
Crosbie, Kimberly - Finite State Au<strong>to</strong>mata <strong>and</strong> an Intrusion De-<br />
tection System<br />
Mack, Richard - Fundamental Theorem of Calculus for Lebesgue<br />
Integration<br />
E207<br />
E103<br />
Mather, Kevin - Dirichlet Series <strong>and</strong> Arithmetic Functions E208<br />
M<strong>and</strong>ryk, Isaiah - Structure of Neural Networks E212<br />
16:00 - 16:30 Coffee Break / Pause café Centre for<br />
16:30 - 17:30 Keynote Speaker / Conférence plénière: Catherine Beau-<br />
chemin - Virologie in Silico: Cultiver des Infections en Ordina-<br />
teur (In Silico Virology: Growing Infections in a Computer)<br />
17 :30 - 18:30 <strong>CUMC</strong> 2013 Host Bids / Enchères pour accueillir le CCÉM 2013<br />
18:30 - 20:30<br />
( section 4.6)<br />
Women in Math <strong>and</strong> Science Dinner (Optional Activity) / Souper<br />
pour les Femmes en Maths et Sciences (Activité facultative)(see<br />
section 2.3)<br />
or<br />
Sc<strong>and</strong>ia (Optional Activity)/(Activité facultative)(see section 2.3)<br />
Saturday July 14, 2012 - Samedi 14 juillet<br />
Learning Atrium<br />
Centre for<br />
Learning Atrium<br />
Centre for<br />
Learning Atrium<br />
Time - Heure Description Room - Local<br />
9:00 - 10:00<br />
Tyson, Rebecca - Opportunities in Mathematical Biology for Grad<br />
Studies<br />
Peterson, David - Investigating Orthogonal Latin Squares Using<br />
Universal Algebra<br />
Dosseva, Annamaria - Galois Theory <strong>and</strong> the Insolvability of the<br />
Quintic<br />
Fipke 124<br />
Fipke 138<br />
Fipke 121<br />
Butson, Dylan - Introduction <strong>to</strong> S<strong>to</strong>chastic Calculus Fipke 140<br />
Arbour, Jean-François - An Overview of Some Elements of Spec-<br />
tral Geometry.<br />
Fipke 250<br />
Park, Hongyoul (Mike) - Diophantine Approximations Fipke 129<br />
Wiebe, Toban - Game Theory <strong>and</strong> Evolution Fipke 133
2.2. COMPREHENSIVE SCHEDULE / HORAIRE DE COMPLÉTER 21<br />
10:00 - 10:30<br />
10:30 - 11:00<br />
Yeremi, Miayan - Statistical refinement of astrophysical numerical<br />
simulations<br />
Kovesi, Michelle - An Introduction <strong>to</strong> Machine Learning for Text<br />
Classification<br />
Weng, Gwen Yun - The Shortest Introduction <strong>to</strong> Semidefinite Pro-<br />
gramming<br />
Fipke 124<br />
Fipke 138<br />
Fipke 121<br />
Martieau, Joanie - Weyls Theorem Fipke 140<br />
Reid, Samuel - Simplicial k-Combina<strong>to</strong>rial <strong>and</strong> Packings: Touch-<br />
ing (k + 1)-tuples of Congruent Balls in 3-space<br />
Davis, Chad - Exploiting Known Structures <strong>to</strong> Approximate Nor-<br />
mal Cones<br />
Lyon, Keenan - Using Symmetry Groups <strong>to</strong> Solve Partial Differ-<br />
ential Equations<br />
Dhawan, Andrew - The Tumor Control Probability <strong>and</strong> Cancer<br />
Stem Cells<br />
Fipke 129<br />
Fipke 124<br />
Fipke 138<br />
Fipke 121<br />
Allan, Kara - A Model of the Spread of MRSA in a Hospital Fipke 140<br />
Sokolowsky, Benjmain - Achieving all Radio Numbers Fipke 129<br />
11:00 - 11:30 Coffee Break / Pause café Fipke Foyer<br />
11:30 - 12:30 Keynote Speaker / Conférence plénière: Dominikus Noll<br />
- On Active <strong>and</strong> Passive Control<br />
Fip 204<br />
12:30 - 14:00 Lunch / Dîner Fipke Foyer<br />
14:00 - 15:00<br />
Lagacé, Jean - Proof of Brouwer Fixed Point Theorm, using<br />
Sperner’s Lemma<br />
Da Silva, Patrick - Fac<strong>to</strong>rial Function : Theorems <strong>and</strong> General-<br />
ization<br />
Chen, Li - A Taste of Homopy Groups <strong>and</strong> Classification of Prin-<br />
cipal Bundels Over S n<br />
Haris, Asad - Introduction <strong>to</strong> Markov Chain Monte Carlo <strong>and</strong><br />
their Applications <strong>to</strong> ODE Models<br />
Huntemann, Svenja - On MDS Codes, the Main Conjecture, <strong>and</strong><br />
the Partition Weight Enumera<strong>to</strong>r<br />
Fipke 124<br />
Fipke 138<br />
Fipke 121<br />
Fipke 140<br />
Fipke 250<br />
Wanless, Michael - Knapsack-Based Cryp<strong>to</strong>graphy Fipke 129<br />
15:00 - 15:30 Coffee Break / Pause café Fipke Foyer
22 CHAPTER 2. SCHEDULE OF EVENTS<br />
15:30 - 16:30 Keynote Speaker / Conférence plénière: Gerda de Vries<br />
- The Language of Life: When Mathematics Speaks <strong>to</strong> Biology<br />
Fip 204<br />
17:30 Closing Banquet Opens / Banquet final Ramada Hotel<br />
18:30-18:45 Closing Remarks / Discours final Ramada Hotel<br />
18:45-19:45 Dinner / Souper Ramada Hotel<br />
19:45-20:00 Announcement of <strong>CUMC</strong> 2013 Host University / L’annonce de<br />
l’université d’accueil - Dessert<br />
Ramada Hotel<br />
20:00-1:00 DANCE DANCE! Ramada Hotel<br />
Sunday July 15, 2012 - Dimanche 15 juillet<br />
Time - Heure Description Room - Local<br />
∀ t ∃x x ∈ <strong>Kelowna</strong>
2.3. ACTIVITIES / ACTIVITÉS 23<br />
2.3 Activities / Activités<br />
Thursday, July 12 - Jeudi le 12 juillet<br />
Ex Nihilo Winery Tour - Tour de cave à vin Ex Nihilo<br />
For those of you who have registered for the Ex Nihilo Winery Tour, your bus will be departing<br />
from the UBC <strong>Okanagan</strong> bus loop at 5pm. Ex Nihilo will be giving us a private <strong>to</strong>ur of their wine<br />
making facilities, art gallery, <strong>and</strong> tasting room. This is a pre-registered event <strong>and</strong> we will not be<br />
taking registration for the event during the conference.<br />
Pour ceux d’entre vous qui se sont inscrits au <strong>to</strong>ur de cave à vin Ex Nihilo, l’au<strong>to</strong>bus partira<br />
de du terminus d’au<strong>to</strong>bus de l’Université de Colombie-Britannique <strong>Okanagan</strong> à 17h. La compagnie<br />
Ex Nihilo nous fera faire un <strong>to</strong>ur privé de ses installations de fabrication du vin, de sa galerie d’art<br />
et de sa salle de dégustation. Pour participer à cet événement, vous devez déjà être inscrit. Les<br />
inscriptions se seront pas possibles durant le congrés.<br />
Movie Night - Soirée de films<br />
For those of you who aren’t feeling adventurous <strong>to</strong>day, we have booked the UBC Students’ Union<br />
Theatre for you <strong>to</strong> come, relax, <strong>and</strong> eat some popcorn (yes there will be popcorn!). The theatre is<br />
located in the University Centre (UNC) building. The show starts at 8pm. We will be showing “A<br />
Dangerous Method".<br />
Pour ceux qui n’ont pas trop le goût d’aventure aujourd’hui, nous avons réservé le UBC Students’<br />
Union Theatre pour que vous puissiez relaxer en mangeant du pop-corn (oui, il y aura du pop-corn!).<br />
Ce cinéma se situe au University Centre (UNC). La projection débutera à 20h et le anglais film<br />
présenté sera “A Dangerous Method".<br />
Friday, July 13 - Vendredi le 13 juillet<br />
Women in Math <strong>and</strong> Science (WIMS) Dinner - Souper pour les Femmes en Maths<br />
et Sciences<br />
The <strong>CUMC</strong> 2012 is pleased <strong>to</strong> continue the tradition of offering a Women in Math <strong>and</strong> Science<br />
(WIMS) Dinner. The theme of this year dinner is “Breaking Down Barriers: Challenges Facing<br />
Female Mathematicians.” The evening will begin with a round table discussion, held in the Centre<br />
for Dialogue in the newly renovated Library at <strong>Okanagan</strong> College, where panelists from both in-<br />
dustry <strong>and</strong> academia will have the chance <strong>to</strong> share their experiences <strong>and</strong> discuss a range of <strong>to</strong>pics.
24 CHAPTER 2. SCHEDULE OF EVENTS<br />
Participants will have ample opportunity <strong>to</strong> join the conversation with their own questions as well.<br />
Afterwards, dinner with be served outside in the Courtyard in the beautiful <strong>Kelowna</strong> sunshine.<br />
During dinner, the participants <strong>and</strong> panelists will be encouraged <strong>to</strong> mingle <strong>and</strong> <strong>to</strong> continue their<br />
conversations.<br />
This year’s organizing committee has decided <strong>to</strong> make the dinner for women <strong>and</strong> woman-<br />
identified participants only. We thank you in advance for respecting our plans.<br />
Le CCÉM de 2012 est heureux de poursuivre la tradition d’offrir le souper Femmes en Maths<br />
et en Sciences. Cette année, le thème du souper est “Briser les barrières : Les Défis Rencontrés par<br />
les Femmes Mathématiciennes.” La soirée commencera par une discussion au “Centre for Dialogue”<br />
dans la partie renovée de la bibliothèque de l’<strong>Okanagan</strong> College. Les panlistes de l’industrie et de<br />
l’académie auront alors la chance de partager leurs expériences et d’aborder plusieurs sujets. Les<br />
participantes sont invitées à participer à la discussion en posant leurs propres questions. Ensuite,<br />
le souper sera servi dans la Cour sous le superbe soleil couchant de <strong>Kelowna</strong>. Pendant le souper,<br />
les participantes et panélistes seront encourages à se mélanger et poursuivre leurs conversations.<br />
Le comité organisateur de cette année a décidé de mettre en place ce souper pour les participantes<br />
seulement. Nous vous remercions à lvance de respecter nos plans.<br />
Sc<strong>and</strong>ia<br />
After our day at <strong>Okanagan</strong> College the 2012 organizing committee has arranged a fun evening<br />
at our local mini-golf <strong>and</strong> games centre, Sc<strong>and</strong>ia (www.sc<strong>and</strong>iagolf<strong>and</strong>games.com). There are retro-<br />
style arcade games, bumper cars, batting cages, <strong>and</strong> loads of mini-golf fun! Mini-golf starts around<br />
$10/game <strong>and</strong> arcade games at 1 <strong>to</strong>ken/game. Buses will be leaving <strong>Okanagan</strong> College at 6:30pm<br />
<strong>and</strong> 7:10pm <strong>to</strong> head <strong>to</strong> Sc<strong>and</strong>ia (enroute <strong>to</strong> UBC <strong>Okanagan</strong>) for an evening of fun. To get back <strong>to</strong><br />
the university take the #97 - UBC <strong>Okanagan</strong> Express from the bus s<strong>to</strong>p across the highway.<br />
Après la journée prévue à l’<strong>Okanagan</strong> College, le comité organisateur 2012 a prévu une soirée<br />
pour se relaxer au centre de jeux et de mini-golf local, Sc<strong>and</strong>ia (www.sc<strong>and</strong>iagolf<strong>and</strong>games.com).<br />
On y retrouve des jeux d’arcade de style rétro, des au<strong>to</strong>s-tamponneuses, des cages de baseball et<br />
du mini-golf à volonté! Le prix du mini-golf commence à environ 10$ par partie et les jeux d’arcade<br />
coûtent un minimum d’un je<strong>to</strong>n par partie. Des au<strong>to</strong>bus partiront de l’<strong>Okanagan</strong> College à 18h30<br />
et à 19h10 pour rejoindre Sc<strong>and</strong>ia, qui se trouve sur le chemin vers l’Université de Colombie-<br />
Britannique <strong>Okanagan</strong>, pour une soirée de plaisir. Pour re<strong>to</strong>urner à lniversité, il suffit de prendre<br />
l’au<strong>to</strong>bus #97 - UBC’s <strong>Okanagan</strong> Express à partir de lrrêt d’au<strong>to</strong>bus de lutre côté de l’au<strong>to</strong>route.
Abstracts / Résumés<br />
3.1 Keynote Abstracts / Résumés plénière<br />
Statistical Excursions in Sport<br />
Dr. Tim Swartz<br />
This talk explores some work that I have done <strong>and</strong> some <strong>to</strong>pics that you may find interesting<br />
with respect <strong>to</strong> statistics in sport. Time permitting, some of the questions that I may cover include:<br />
When should you pull your goalie in hockey?<br />
Was the draft in the Indian Premier League (cricket) sensible?<br />
Do competitive Highl<strong>and</strong> dancers perform in a fair order?<br />
Is there an age effect in minor hockey?<br />
When should you gamble in sports?<br />
An Invitation <strong>to</strong> Projection Methods<br />
Dr. Heinz H. Bauschke<br />
Feasibility problems, i.e., finding a solution satisfying certain constraints, are common in mathe-<br />
matics <strong>and</strong> the natural sciences. If the constraints have simple projec<strong>to</strong>rs (nearest point mappings),<br />
then one approach is <strong>to</strong> use these projec<strong>to</strong>rs in some algorithmic fashion <strong>to</strong> approximate a solution.<br />
In this talk, I will survey three methods (alternating projections, Dykstra, <strong>and</strong> Douglas- Rach-<br />
ford), <strong>and</strong> comment on recent advances <strong>and</strong> remaining challenges.<br />
25
26 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
To All the Graphs I’ve Loved Before<br />
Dr. Donovan Hare<br />
What inspires me? Love inspires me. And me loves the graphs.<br />
I will show you some graphs I especially love <strong>and</strong> the problems they come from. Be warned: I’m<br />
not talking about graphing functions. No, I’m talking about the structure of love - relationships -<br />
<strong>and</strong> what can be dished about them.<br />
Sound crazy? It is. But then so is love.<br />
Finite Bases of Quasi-equations of Unary Algebras: How Few<br />
Rules Can We Get Away With<br />
Dr. Jennifer Hyndman<br />
The associative, distributive, commutative, negation <strong>and</strong> identity laws (equations) for the in-<br />
tegers are fundamental <strong>to</strong> our underst<strong>and</strong>ing of the integers. From childhood we “know" that<br />
everything follows from these laws. When we move <strong>to</strong> another algebraic structure a natural ques-<br />
tion is <strong>to</strong> ask what are the equations that hold <strong>and</strong> from which equations does everything else<br />
follow?<br />
When we allow for implications as well as equality we are considering expressions called quasi-<br />
equations. Sometimes when working with small algebraic structures with, say, 4 or 5 elements, our<br />
natural instinct that a few quasi-equations are sufficient <strong>to</strong> imply all quasi-equations is true. In<br />
other instances we require initely many quasi-equations <strong>to</strong> generate all quasi-equations. In this talk<br />
we see the variety of results that can arise in the seemingly simple situation of quasi-equations of<br />
small algebraic structures with only unary operations.<br />
Virologie in silico: cultiver des infections en ordinateur<br />
(In silico virology: growing infections in a computer)<br />
Dr. Catherine A.A. Beauchemin<br />
French talk with English slides<br />
L’expérimentation in vitro ou in vivo a longtemps éeté la seule et unique fa con d’étudier<br />
les infections virales. Cette méthode d’apprentissage est essentiellement fondée sur des postulats<br />
rarement contestés, du fait qu’il est diffcile detudier séparément une des composantes de ces systémes<br />
complexes sans en affecter une autre. Heureusement, les modéles mathématiques et informatiques
3.1. KEYNOTE ABSTRACTS / RÉSUMÉS PLÉNIÈRE 27<br />
nous permettent de déconstruire le système expérimental a d’identir ses composantes principales et<br />
de déterminer de quelle facon elles doivent être recombinées a de recréer la dynamique observée en<br />
labora<strong>to</strong>ire.<br />
Dans cet exposé, je présenterai des exemples de modèles mathématiques qui remettent en ques-<br />
tion la validité de certaines expériences d’infections in vitro et des exemples d’expériences in vitro<br />
qui nous forcent à revoir nos expressions mathématiques préférées.<br />
Experimentation in vitro <strong>and</strong> in vivo has traditionally been the only way <strong>to</strong> study viral infec-<br />
tions. This approach for deriving knowledge often relies on “common-sense" assumptions that go<br />
unchallenged due <strong>to</strong> the difficulties involved in controlling components of these complex systems<br />
without affecting others. Mathematical <strong>and</strong> computer models, however, make it possible <strong>to</strong> de-<br />
construct an experimental system in<strong>to</strong> individual components <strong>and</strong> determine how the pieces come<br />
<strong>to</strong>gether <strong>to</strong> recreate the observed behaviour.<br />
In this talk, I will give examples of math models that challenge the validity of certain in vitro<br />
infection experiments, <strong>and</strong> of experiments that force us <strong>to</strong> consider more difficult math.<br />
On Active <strong>and</strong> Passive Control<br />
Dr. Dominikus Noll<br />
We will discuss passive control, also known as optimal control, <strong>and</strong> active control, also referred <strong>to</strong><br />
as feedback control. We ask when these techniques are applied, what they have in common, in which<br />
sense they are complementary, <strong>and</strong> we discuss the mathematical techniques used <strong>to</strong> characterize<br />
<strong>and</strong> compute these control laws.<br />
The Language of Life: When Mathematics Speaks <strong>to</strong> Biology<br />
Dr. Gerda de Vries<br />
Mathematics often is described as the language of science, particularly suited <strong>to</strong> speak <strong>to</strong> prob-<br />
lems in physics, chemistry, engineering, <strong>and</strong> so on. Is mathematics also the language of life, suited<br />
<strong>to</strong> speak <strong>to</strong> problems in biology? Indeed, mathematics has a long <strong>and</strong> rich his<strong>to</strong>ry in biology, <strong>and</strong><br />
the reality is that <strong>to</strong>day biology depends increasingly on data, algorithms, <strong>and</strong> models; mathemat-<br />
ics plays an extremely important role in biology. In this talk, I will highlight some particularly<br />
noteworthy his<strong>to</strong>rical contributions of mathematics in biology, dating back <strong>to</strong> the late 1600, make<br />
connections <strong>to</strong> contemporary research in mathematical biology, <strong>and</strong> discuss how this research im-<br />
pacts our lives.
28 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
3.2 Student Abstracts / Résumés des étudiants<br />
The student talks are arranged in alphabetical order by the speaker’s last name. The presentation<br />
will be in the language of the abstract, except if a note says otherwise.<br />
Les présentations étudiantes sont classées en ordre alphabétique selon le nom de famille de l’orateur.<br />
Elles seront présentées dans la même langue que le résumé, sauf si une note indique le contraire.<br />
An Irreducibility Criterion of A. Cohn<br />
Abdullah Al-Shaghay<br />
This talk explores an interesting irreducibility criterion, which is attributed <strong>to</strong> Arthur Cohn,<br />
for a particular subset of polynomials belonging <strong>to</strong> the ring Z[x]. I hope <strong>to</strong> discuss the significance<br />
of the theorem, examples of applying the theorem, <strong>and</strong> a conjecture which is closely related <strong>to</strong> the<br />
theorem.<br />
A Model Of The Spread of MRSA In A Hospital<br />
Kara Allan<br />
MRSA is a serious problem in most hospitals throughout the world. It is spread primarily by<br />
health care workers. This talk focuses on the model that I have been building since last summer <strong>to</strong><br />
represent the spread of this disease. I use a s<strong>to</strong>chastic SIS model with the population divided in<strong>to</strong><br />
patients <strong>and</strong> healthcare workers. The patients are further divided by rooms. I assume that there is<br />
no contact between patients, so that the healthcare worker is acting as the vec<strong>to</strong>r for transmission<br />
between patients. I will be studying the distribution of the time <strong>to</strong> extinction <strong>to</strong> underst<strong>and</strong> the<br />
effects of intervention by healthcare workers.<br />
An overview of the some elements of spectral geometry<br />
Jean-François Arbour<br />
There are a lot of approaches <strong>to</strong> study a geometric object. Probably the most important idea<br />
for this has been the introduction of coordinates <strong>to</strong> view our geometric object as the solution of an<br />
equation of some sort, linking the geometry with algebra or calculus. In this talk, I will describe<br />
another approach: that of spectral geometry. Say you want <strong>to</strong> tell two r<strong>and</strong>om geometric objects<br />
apart. Well, a spectral geometer may be inclined <strong>to</strong> throw rocks at them <strong>and</strong> decide they are not<br />
the same if they don’t make the same noise! Another spectral geometer may put them on fire, put
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 29<br />
one h<strong>and</strong> on each objects, <strong>and</strong> decide they are not the same if he burns his left h<strong>and</strong> first! Put it<br />
briefly, I will describe <strong>to</strong> you some of the finest technological <strong>to</strong>ols we have <strong>to</strong> do geometry.<br />
Required background: First year undergraduate mathematics.<br />
Steiner Symmetriations: Convergence <strong>and</strong> Rate of Convergence<br />
Reza Asad<br />
Steiner symmetrization was invented in the 19 century as a <strong>to</strong>ol for proving the isoperimetric<br />
inequality. The isoperimetric problem in the plane says that among all closed <strong>and</strong> simple curves<br />
of fixed length, the circle <strong>and</strong> only the circle encloses the most area. In the 1970, rearrangements<br />
like Steiner symmetrization gained new interest, because they proved <strong>to</strong> be useful for less obvious<br />
minimization problems in functional analysis.<br />
Steiner Symmetrization manipulates the shape of a body (or a function) without changing its<br />
size (norm). It is a classical fact that given an arbitrary convex body, there exists an appropriate<br />
sequence of Steiner symmetrizations that transforms it <strong>to</strong> a Euclidean ball. How well is full radial<br />
symmetrization approximated by sequences of such rearrangements? How fast do these sequences<br />
converge? These questions are subtle, because Steiner symmetrizations are neither linear, nor<br />
spatially localized <strong>and</strong> typically do not commute.<br />
In this talk, I will discuss works of a former U of T Master student Marc Fortier regarding<br />
Steiner symmetrizations applied <strong>to</strong> continuous functions with compact support. I will also state<br />
an open problem regarding the rate of convergence of such sequences of Steiner symmetrizations.<br />
Lastly, I will introduce ideas on how <strong>to</strong> approach the open problem.<br />
Required Background: Basic Analysis <strong>and</strong> Algebra<br />
Special Functions <strong>and</strong> Orthoganal Polynomials<br />
Micheal Baker<br />
I will give a lucid exposition of the theory of special functions <strong>and</strong> orthogonal polynomials<br />
(spherical harmonics, in particular, will be emphasized). The talk will be his<strong>to</strong>rically motivated by<br />
classical problems from mathematical physics. Some modest complex analysis will inevitably be a<br />
prerequisite.
30 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
Abelian <strong>and</strong> Additive Complexity: Analyzing Structure in Infinite<br />
Words<br />
Graham Banero<br />
Motivated by the problem of avoidability of abelian <strong>and</strong> additive squares, notions of the abelian<br />
<strong>and</strong> additive complexity of an infinite word w over a finite alphabet have been introduced as follows.<br />
The abelian complexity ρ ab (w, n) counts the maximum number of fac<strong>to</strong>rs of w having length n, such<br />
that no two are permutations of each other; the additive complexity ρ Σ (w, n) counts the number<br />
of distinct sums of fac<strong>to</strong>rs of w with length n. We give an overview of some main results on<br />
these relatively new concepts, paying attention in particular <strong>to</strong> the rich similarities <strong>and</strong> surprising<br />
differences between the two.<br />
Scaling Arguments on the Space of Connections<br />
Matthew Beckett<br />
The intent of this talk is <strong>to</strong> introduce Derrick scaling arguments. I will begin by giving give<br />
a (very) brief introduction <strong>to</strong> connections <strong>and</strong> deing the curvature form so that we are able <strong>to</strong><br />
introduce the Yang-Mills action.We will work with the speci example of the Yang-Mills action, deed<br />
on the space of connections, <strong>to</strong> show how by rescaling the base space <strong>and</strong> then observing how this<br />
effects the action we can learn interesting information about critical points. Some prior knowledge<br />
of differential forms will be helpful, but not necessary.<br />
Principal Component Analysis <strong>and</strong> its Application <strong>to</strong> High Dimensional<br />
data Sets<br />
Nikolina Beg<br />
Data sets are getting bigger <strong>and</strong> bigger, with more <strong>and</strong> more variables. What can you do when<br />
your data set is so large you can analyze it efficiently? Principal Component Analysis (PCA) is a well<br />
known multivariate technique that can lead <strong>to</strong> effective dimension reduction, allowing statisticians<br />
<strong>to</strong> analyze their data set efficiently without losing information from the data. The concepts behind<br />
Principal Component Analysis will be introduced <strong>and</strong> its mathematical background explored, as<br />
well as how visualization techniques can be used <strong>to</strong> generate a better underst<strong>and</strong>ing of results.<br />
Then, the problem of dimension reduction on high dimensional data sets, specifically where p ≫ N,<br />
will be explored. Variations of PCA, such as Supervised Principal Components, will be investigated
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 31<br />
in order <strong>to</strong> underst<strong>and</strong> how a sub-sampling approach <strong>to</strong> a large problem can produce usable results<br />
<strong>and</strong> information.<br />
What is Underst<strong>and</strong>ing?<br />
Rene Bidart<br />
What does it mean when someone says they underst<strong>and</strong> something? Is it the same for everyone<br />
or do people underst<strong>and</strong> in different ways? why do some people excel when presented with rigorous<br />
proofs, which others simply could not grasp? this presentation will discuss the way in which people<br />
learn or underst<strong>and</strong> “abstract” math, such as group theory, <strong>and</strong> more elementary <strong>to</strong>pics in mathe-<br />
matics, such as basic arithmetic. It will consider the concept that underst<strong>and</strong>ing is visualization,<br />
along with the other possible ideas of what learning is.<br />
Calcul formel et programmation / Programming Computer Algebra<br />
Nicolas Bouchard<br />
Aujourd’hui, personne ne peut se passer d’ordinateurs, pas même les mathématiciens. Les<br />
logiciels, tels que Mathematica ou Maple, sont de plus en plus sophistiqués et permettent de faire<br />
des choses inouïes. Ils permettent de dériver des expressions complexes, ils peuvent jongler avec<br />
des groupes et même calculer des séries de Taylor. Mais comment? Ce n’est pas de la magie, c’est<br />
de la programmation!<br />
Nowadays, everybody uses a computer, even mathematicians. Softwares like Mathematica <strong>and</strong><br />
Maple are getting more <strong>and</strong> more sophisticated <strong>and</strong> can do things quite unexpected. For instance,<br />
they can differentiate most expressions of any degree of complexity, they can use group theory, <strong>and</strong><br />
even compute Taylor expansion. How? It is not magical, it is programming!<br />
Introduction <strong>to</strong> S<strong>to</strong>chastic Calculus<br />
Dylan Butson<br />
In the deterministic setting of real analysis one may dee the Riemann Stieltjes integral, which<br />
integrates one function with respect <strong>to</strong> another. In analogy with this, one can dee the integral of<br />
one s<strong>to</strong>chastic process with respect <strong>to</strong> another, which is itself a new r<strong>and</strong>om process. Such integrals<br />
can be used <strong>to</strong> give meaning <strong>to</strong> s<strong>to</strong>chastic di?erential equations <strong>and</strong> in many ways these ob jects
32 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
behave similarly <strong>to</strong> their deterministic counterparts. I introduce these concepts <strong>and</strong> motivate the<br />
key basic results of the sub ject. Topics include: Necessary background in the theory of s<strong>to</strong>chastic<br />
processes; the Riemann-Stieltjes integral; the I<strong>to</strong> integral; properties of the integral process; the I<strong>to</strong><br />
formula; examples throughout.<br />
Required Background: Only a knowledge of basic probability is assumed, but background in real<br />
analysis <strong>and</strong> s<strong>to</strong>chastic processes will be useful.<br />
Cyclo<strong>to</strong>mic Polynomials <strong>and</strong> Elementary Number Theory<br />
Manuel C<strong>and</strong>ales<br />
The n-th cyclo<strong>to</strong>mic polynomial Φn(x), (n a positive integer) is the monic polynomial Φn(x) =<br />
� (x−ζ) where ζ runs over all the n-th primitive roots of unity. It is an integer polynomial, <strong>and</strong> it is<br />
irreducible in Z[x]. The polynomial x n −1 fac<strong>to</strong>rs in Z[x] in the following way: x n −1 = �<br />
d|n Φd(x).<br />
His<strong>to</strong>rically, the cyclo<strong>to</strong>mic polynomials (<strong>and</strong> cyclo<strong>to</strong>mic number fields) have played a very<br />
important role in mathematics, because of their connection <strong>to</strong> fundamental problems, such as the<br />
constructibility of regular polygons <strong>and</strong> Fermat’s Last Theorem.<br />
In this talk we will discuss the applications of cyclo<strong>to</strong>mic polynomials <strong>to</strong> solve problems in<br />
elementary number theory. We will introduce them <strong>and</strong> present some of their elementary properties.<br />
We will then use them <strong>to</strong> give elementary proofs of problems such as the infinitude of primes<br />
congruent <strong>to</strong> 1 modulo n (which is a special case of Dirichlet’s theorem on arithmetic progressions).<br />
Required Background: If you have some familiarity with elementary number theory <strong>and</strong> unders<strong>to</strong>od<br />
the first paragraph, then you are in good shape.<br />
DFAs, Au<strong>to</strong>matic Numbers, <strong>and</strong> Transcendence<br />
Ian Charlesworth<br />
A common object within the theory of computing is the Deterministic Finite Au<strong>to</strong>ma<strong>to</strong>n (DFA);<br />
roughly <strong>and</strong> informally, a DFA is like a computer with a finite (<strong>and</strong> often small) amount of memory<br />
available. These give rise <strong>to</strong> the definition of an au<strong>to</strong>matic sequence as one which can be generated<br />
by a DFA, <strong>and</strong> an au<strong>to</strong>matic real number in base-b as one whose base-b expansion is au<strong>to</strong>matic.<br />
After introducing these concepts more rigorously, we will demonstrate a recent result of Boris<br />
Adamczewski <strong>and</strong> Yann Bugeaud from 2007: that any au<strong>to</strong>matic number is either rational or<br />
transcendental.
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 33<br />
Required background: Prior exposure <strong>to</strong> au<strong>to</strong>matic numbers or sequences is not expected; ex-<br />
perience with DFAs will add <strong>to</strong> the talk, but the talk should still be accessible without it <strong>and</strong> they<br />
will be covered briefly at the start of the talk.<br />
Temperley Lieb Algebras<br />
Philippe Charron<br />
What happens when you take a vec<strong>to</strong>r space <strong>and</strong> embed it with some kind of vec<strong>to</strong>r multipli-<br />
cation? You get an algebra, which is a well-studied algebraeic object (no pun intended). I will<br />
introduce the Temperley-Lieb algebras, a family of algebras that were introduced <strong>to</strong> modelize cer-<br />
tain phase transitions <strong>and</strong> ice phenomenons in physics. Also, despite being ugly looking they admit<br />
a very natural visual presentation, which I will investigate in greater detail.<br />
A Taste of Homopy Groups <strong>and</strong> Classifications of Principal<br />
Bundels over S n<br />
Li Chen<br />
It seems so that mathematicians pursued after their agenda of pure abstractions while the<br />
physicists had less interest in the mathematical generalizations. The great divorce of mathematics<br />
<strong>and</strong> physics might have just occurred after their first rendez-vous in ancient Babylon. But when<br />
Einstein made his theory of general relativity, it seems that physics <strong>and</strong> mathematics came <strong>to</strong>gether<br />
once more as laws of nature are written by strokes of differential geometry. More than that, but<br />
the s<strong>to</strong>ry that we are going <strong>to</strong> tell is one that is even more profound. It is what physicists call<br />
gauge fields. In this short talk, however, we will only venture <strong>to</strong> speak of the two basic concepts:<br />
homo<strong>to</strong>py groups <strong>and</strong> principal bundles. In particular, we will classify principal bundles over S n . If<br />
time permits, we will introduce connections on principal bundle, Yang-Mill functional, <strong>and</strong> matter<br />
fields.<br />
Finite State Au<strong>to</strong>mata <strong>and</strong> an Intrusion Detection System<br />
Kimberly Crosbie<br />
An Intrusion Detection System (IDS) is used <strong>to</strong> help protect computer networks from attacks<br />
<strong>and</strong> intrusions. One specific type of IDS is called signature-based network IDS. This kind of IDS<br />
moni<strong>to</strong>rs network traffic in search of malicious activity as specified in attack descriptions (referred <strong>to</strong>
34 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
as signatures). It has been discovered that several of these signatures can be triggered by the same<br />
set of packets, a situation which has been referred <strong>to</strong> as overlapping signatures. It has been shown<br />
that attacks on networks can occur by exploiting overlapping signatures. After a brief introduction<br />
<strong>to</strong> basic finite state au<strong>to</strong>mata theory, this talk will look at overlapping signatures in a commonly<br />
used IDS called Snort. By using set theory <strong>and</strong> finite state au<strong>to</strong>mata theory we will see how it is<br />
possible <strong>to</strong> quantify this overlapping signature problem.<br />
Predicting the Spatial Distribution of an Orchard Insect<br />
Pest<br />
Garrett Culos<br />
Codling moth is a pest which has plagued agriculturalists for the better part of the last century.<br />
Attempts in controlling this pest were successful until early 2000’s when of some mysterious reason<br />
the wild population began <strong>to</strong> increase. In an attempt <strong>to</strong> better underst<strong>and</strong> this invasive pest a model<br />
was used <strong>to</strong> predict the percent of codling moths at arbitrary distance from there release point.<br />
This model is a deterministic diffusion-based partial differential equation which allows switching<br />
between two different movement modes. We used the experimental data <strong>to</strong> validate this model.<br />
Using the negative log-likelihood function <strong>and</strong> a recursive cubical division of parameter space <strong>to</strong> fit<br />
the data we obtained some extraordinary insight in<strong>to</strong> the codling moth behaviour.<br />
Fac<strong>to</strong>rial Function : Theorems <strong>and</strong> Generalization<br />
Patrick Da Silva<br />
As it st<strong>and</strong>s <strong>to</strong>day, mathematicians in general know very few things of the fac<strong>to</strong>rial function<br />
outsidethe fact that it appears in the denomina<strong>to</strong>r of the terms in the Taylor expansion of an<br />
analytic function, the binomial coefficients <strong>and</strong> counting interpretations. In his paper, Manjul<br />
Bhargava wrote a paper which is generalizing the fac<strong>to</strong>rial function <strong>and</strong> exploring not-so-well-<br />
known theorems involving the fac<strong>to</strong>rial function. We will see that his generalization of the fac<strong>to</strong>rial<br />
function is quite natural from a number-theoretic point of view, <strong>and</strong> many questions arise from his<br />
paper. I will try <strong>to</strong> explain the theorems <strong>and</strong> the reasons behind the deitions of Manjul Bhargava.<br />
His paper can be found online by typing “ManjulBhargava Fac<strong>to</strong>rial” on Google.
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 35<br />
Exploiting Known Structures <strong>to</strong> Approximated Normal Cones<br />
Chad Davis<br />
The normal cone <strong>to</strong> a constraint set plays a key role in optimization theory. We consider the<br />
question of how <strong>to</strong> approximate the normal cone <strong>to</strong> a set under the assumption that the set is<br />
provided through an oracle function or collection of oracle functions, but contains some exploitable<br />
structure. We provide a new simplex gradient based approximation technique that works for sets<br />
of the form<br />
S = {x � � gi(x) ≤ 0, i = 1, . . . , N}<br />
where each gi : R n → R is unknown <strong>and</strong> provided by an oracle. We further present novel results<br />
showing that, under a non-degeneracy condition, approximating normal cones <strong>to</strong> intersections of sets<br />
is possible by taking sums of approximations. Finally, we provide numerical results that exemplify<br />
the accuracy of the simplex gradient approximation when it is applicable, <strong>and</strong> the failure of this<br />
technique when a linear independence constraint qualification is not met.<br />
Connexions et calcul rigourex<br />
Andréa Deschênes<br />
Le calcul des solutions d’équations différentielles représente souvent un défi pour les scientifiques.<br />
En effet, les méthodes permettant de trouver ces solutions analytiquement s’appliquent rarement.<br />
Mais que faire lorsque la théorie ne nous permet pas d’aller plus loin? On doit alors mélanger les<br />
mathématiques numériques à l’analyse! Dans cet exposé, nous montrerons comment utiliser le calcul<br />
rigoureux pour trouver une connexion, un type particulier de solution d’une équation différentielle<br />
ordinaire. Pour ce faire, nous introduirons la notion de connexions homoclines et hétéroclines. Puis,<br />
les gr<strong>and</strong>es étapes d’une méthode de calcul rigoureux seront présentées. Cette méthode permet de<br />
prouver, grâce à l’ordinateur et à l’analyse, l’existence d’une vraie connexion dans un voisinage<br />
au<strong>to</strong>ur de celle trouvée de manière numérique. Posséder quelques connaissances de base sur les<br />
équations différentielles représentera un a<strong>to</strong>ut pour comprendre cette présentation.<br />
The Tumor Control Probability <strong>and</strong> Cancer Stem Cells<br />
Andrew Dhawan<br />
This talk will provide an introduction <strong>to</strong> the mathematics underlying the tumor control prob-<br />
ability (TCP), as well as the relevant cancer biology, as they are used within the planning <strong>and</strong><br />
modeling of radiotherapeutic treatments for cancer. The TCP is a formalism derived <strong>to</strong> compare
36 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
various treatment regimens of radiation therapy, <strong>and</strong> gives the probability that a prescribed dose of<br />
radiation eradicates, or controls, a tumor. The focus of this talk will be the development of a novel<br />
TCP model <strong>to</strong> account for the presence of cancer stem cells - a critically important subpopulation<br />
of cells found within the tumor mass. Such cancer stem cells are thought <strong>to</strong> drive the proliferation<br />
of the tumor, as they possess an unlimited replicative potential. Moreover, by analyzing tumor<br />
control through the control of stem cells, this talk will cover how this formulation of the TCP can<br />
be used in practice as a measurable quantity, as opposed <strong>to</strong> a theoretical one, via the results of<br />
immunohis<strong>to</strong>chemical assays.<br />
Galois Theory <strong>and</strong> the Insolvability of the Quintic<br />
Annamaria Dosseva<br />
Methods for solving some quadratic equations were known since Babylonian times, around 300<br />
B.C., though the quadratic formula as we know it <strong>to</strong>day was not discovered until around the ninth<br />
century, by the Persian mathematician al-Khowârizmî. The solution is outlined in his Algebra using<br />
the Greek method of geometry – our modern complete the square method. Over the next several<br />
hundred years, other mathematicians searched for a cubic formula that could be used <strong>to</strong> solve cubic<br />
equations, similar <strong>to</strong> the quadratic formula for quadratic equations. The solutions <strong>to</strong> the cubic <strong>and</strong><br />
quartic were found during the 1500s through a combined effort of mathematicians at the Italian<br />
Mathematical School at Bologna.<br />
For nearly 300 years after that, algebraists searched for a general equation of the fifth degree.<br />
Paolo Ruffini (1765-1822) first proved that there is no general solution; Niels Henrik Abel (1802-<br />
1829) proved it as well, using a more rigorous argument than Ruffini’s; finally, Évariste Galois<br />
(1811-1832) showed the precise conditions for when a quintic – <strong>and</strong>, in general, for when an alge-<br />
braic equation of any degree – could be expressed as a finite number of additions, subtractions,<br />
multiplications, divisions, <strong>and</strong> a finite extraction of roots.<br />
Before discussing the problem, we will briefly review some of the language <strong>and</strong> theory of Abstract<br />
Algebra, namely the theories of Groups, Rings, Fields, Vec<strong>to</strong>r Spaces, <strong>and</strong> some Galois Theory.<br />
However, “Galois Theory is like garlic in that there is no such thing as a little of it. One must make<br />
a substantial study of it <strong>to</strong> appreciate the reasoning" (Carl B. Boyer).<br />
Required Background: A previous exposure <strong>to</strong> Groups, Rings, Fields <strong>and</strong> Vec<strong>to</strong>r Spaces will be<br />
useful, although not necessary as they will be covered briefly.
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 37<br />
Rate of Convergence of R<strong>and</strong>om Polarizations<br />
Anne Dranovski<br />
His talk will give a description of simple rearrangements known as polarizations, or two-point<br />
symmetrizations, <strong>and</strong> an outline of a convergence problem which is the <strong>to</strong>pic of a summer research<br />
project.<br />
Required Background: basic analysis <strong>and</strong> probability.<br />
Supplemental Learning: A New Way <strong>to</strong> Learn Mathematics!<br />
Jodie Foster<br />
Supplemental Learning (SL) is a peer lead program that targets his<strong>to</strong>rically difficult courses in<br />
order <strong>to</strong> help students improve their underst<strong>and</strong>ing of course material. In particular, it allows stu-<br />
dents <strong>to</strong> get <strong>to</strong>gether <strong>to</strong> discuss important concepts <strong>and</strong> develop strategies for studying the subject.<br />
Supplemental Learning Leaders are exceptional students who have taken the course previously <strong>and</strong><br />
are prepared <strong>to</strong> share what they have learned over the years when studying that particular <strong>to</strong>pic.<br />
SL applies techniques such as: turning questions, student teaching, <strong>and</strong> the Boardwork Model. SL<br />
is not limited <strong>to</strong> only mathematics, but also in an assortment of subjects such as applied science,<br />
art his<strong>to</strong>ry, biology, chemistry, geography, human kinetics, physics <strong>and</strong> psychology. Who are we if<br />
not professional learners? It is up <strong>to</strong> us <strong>to</strong> lend ourselves <strong>and</strong> our undergraduate experiences <strong>to</strong><br />
those just beginning <strong>to</strong> immerse themselves in<strong>to</strong> the world of mathematics.<br />
Stabilization Time for a Type of Evolution on Binary Strings<br />
Jacob Funk<br />
We consider a type of evolution on {0, 1} n inspired by an elementary question about a line<br />
of soldiers, each of whom are attempting <strong>to</strong> find the right direction <strong>to</strong> face. Mathematically, we<br />
consider a string consisting of n binary bits, <strong>and</strong> engage in a process of simultaneously replacing<br />
every instance of “01” in this string with “10”. By doing so, new instances of “01” are created<br />
(for instance “0101” ↦→ “1010”, with a new instance of “01” appearing in the middle). Thus the<br />
same operation as above can be performed on the new string that was obtained, <strong>and</strong> so on. It is<br />
elementary <strong>to</strong> show that this process of recursively creating new strings stabilizes after at most n−1<br />
iterations, with the final string being of the form 11 · · · 1100 · · · 00. The time of stabilization for a<br />
r<strong>and</strong>om string in {0, 1} n is thus a r<strong>and</strong>om variable with values in {0, 1, . . . , n − 1}. My talk will
38 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
present results describing the asymp<strong>to</strong>tic behaviour of this r<strong>and</strong>om variable for n → ∞. The <strong>to</strong>ols<br />
used in the arguments are a natural interpretation of strings in {0, 1} n as Young diagrams, <strong>and</strong> a<br />
connection with the known distribution for the maximal height of a Brownian path on [0, 1]. This<br />
is a joint project with Mihai Nica <strong>and</strong> Michael Noyes, <strong>and</strong> is part of my current NSERC USRA<br />
term in the Pure Mathematics Department at Waterloo.<br />
Introduction <strong>to</strong> Modular Forms<br />
Mathilde Gerbelli-Gauthier<br />
The aim of this talk will be <strong>to</strong> give an intuitive introduction <strong>to</strong> a class of highly symmetric<br />
complex functions: Modular Forms. In order <strong>to</strong> do this, we will study the group of au<strong>to</strong>morphisms<br />
of the complex upper half-plane <strong>and</strong> its discrete subgroups. This will allow us <strong>to</strong> dee modular<br />
forms, <strong>to</strong> derive some of their properties, <strong>and</strong> <strong>to</strong> get a glimpse of their relation <strong>to</strong> number theory.<br />
Drawings included!<br />
Required background: complex numbers, familiarity with groups.<br />
Introduction à l’Homologie Singuliére<br />
Kevin Gervais<br />
En <strong>to</strong>pologie, il peut être très difficile de déterminer si deux espaces donnés sont différents l’un<br />
de l’autre. Une technique très efficace qui nous permet de diffé rencier les espaces <strong>to</strong>pologiques<br />
consiste à associer aux espaces une structure algébrique. Les groupes d’homologie en sont un bel<br />
exemple. Non seulement permettent-ils de différencier (à homo<strong>to</strong>pie près) les espaces <strong>to</strong>pologiques,<br />
ils permettent ègalement d’offrir des preuves très élégantes pour de nombreux théorèmes, tels que :<br />
le théorème du point e de Brouwer, le théorème de Jordan et l’invariance de la dimension. Je propose<br />
donc de vous introduire aux groupes d’homologie et de présenter certaines de leurs propriétés.<br />
Analysis around Fractals<br />
Jonathan Godin - Engish talk with French slides<br />
How can we create a fractal? This presentation will introduce some useful analysis <strong>to</strong>ols such<br />
as metric spaces, Hausdorff distance, <strong>and</strong> iterated function system (IFS) so that we can create<br />
some interesting sets in R 2 . Basic real analysis knowledge such as convergence of a sequence <strong>and</strong><br />
continuity are necessary for a better underst<strong>and</strong>ing of the concepts.
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 39<br />
Introduction <strong>to</strong> Markov Chain Monte Carlo <strong>and</strong> their application<br />
<strong>to</strong> ODE models<br />
Asad Haris<br />
Markov Chain Monte Carlo (MCMC) methods have long been used <strong>to</strong> simulate samples from<br />
a given target distribution. In the past few decades numerous MCMC algorithms have been de-<br />
veloped <strong>and</strong> improvements have been made <strong>to</strong> the existing algorithms. This talk will begin with<br />
a short introduction <strong>to</strong> Bayesian statistics, the theory of Markov Chains <strong>and</strong> a brief description of<br />
certain basic MCMC algorithms. In Bayesian Statistics, on many occasions, we obtain only partial<br />
knowledge about the distribution of a r<strong>and</strong>om variable. The first part of the talk will focus on<br />
such circumstances <strong>and</strong> hence lead <strong>to</strong> the discussion on the motivation of sampling techniques <strong>and</strong><br />
MCMC methods.<br />
In the second part of the talk I will demonstrate the use of Bayesian computational <strong>to</strong>ols <strong>to</strong><br />
estimate parameters in an Ordinary Differential Equation (ODE) Model. ODE models can are used<br />
in many sciences <strong>to</strong> model numerous systems <strong>and</strong> in many cases have many parameters associated<br />
with the model. Due <strong>to</strong> multiple parameters, the usual sampling techniques prove <strong>to</strong> be inefficient<br />
<strong>and</strong> hence advanced MCMC methods are used. This talk will review <strong>and</strong> compare some of the<br />
recent advancements <strong>to</strong> MCMC algorithms. The model under consideration will be the Fitz-Hugh<br />
Nagumo Model which aptly demonstrates the usual computational problems associated with such<br />
problems of parameter estimation.<br />
Finally, I will discuss my current research <strong>and</strong> possible ideas for future research. This talk will<br />
assume only a basic knowledge of probability <strong>and</strong> is open <strong>to</strong> all interested in applied computational<br />
statistics.<br />
Exponential Model of the Eiffel Tower<br />
Josh Holt, Richard Hudson, Bryan Zintel<br />
Equations modeling the shape of the Eiffel Tower are investigated. We have developed an<br />
exponential model based on the equilibrium of moments <strong>and</strong> embodied wind load on the <strong>to</strong>wer.<br />
The result yields an exponential profile of the <strong>to</strong>wer. We analyze the actual Eiffel Tower Profile<br />
<strong>to</strong> show that this profile may be closely approximated by two piecewise exponential curves with<br />
different growth rates.
40 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
Qualitative Analysis of Chemical Reaction Networks<br />
Joseph Horan<br />
We are often interested in investigating non-linear dynamical systems, which are nigh impossible<br />
<strong>to</strong> solve explicitly for the most part; however, there exist numerous methods of qualitative analysis<br />
we can use <strong>to</strong> determine if there are equilibrium points or periodic orbits, on which subspaces<br />
do solutions reside, <strong>and</strong> how stable limit points/sets are, amongst other things. One particular<br />
class of non-linear systems which is interesting is that of chemical reaction networks; this is the<br />
subject of my summer research. Here, I briefly review the notation for such systems, <strong>and</strong> in<br />
a survey style, present a pseudo-graph-theoretic approach developed by Vol’pert, as well as the<br />
row/column diagonal dominance Lyapunov method developed by many, all illustrated by the same<br />
simple example, that of the enzyme model. A method for finding conservation relations, by Schuster<br />
<strong>and</strong> Höfer, is also discussed. I posit questions for the future, due <strong>to</strong> the open nature of the field.<br />
The convergence criterias of the bayesian Monte Carlo Simulation<br />
on the quantification of the number of fluorophores in<br />
a cell<br />
Chieh-Ting(Jimmy) Hsu<br />
Pho<strong>to</strong>bleaching of fluorophores in a cell e.g. Green Fluorescent Protein(GFP) is a s<strong>to</strong>chastic<br />
process, which is similar <strong>to</strong> radioactive decay. Though it leads <strong>to</strong> an exponential decay on average,<br />
the fluctuations away from the average exponential decay are not white noise, so traditional least-<br />
squares fits of the decay are not appropriate. Since the fluctuations are due <strong>to</strong> the pho<strong>to</strong>bleach<br />
events, we can use them <strong>to</strong> quantify the number of fluorophores in a cell. To extract the fluctua-<br />
tions we need the average decay, however real pho<strong>to</strong>bleach data of bacteria expressing GFP shows<br />
s<strong>to</strong>chastic exponential decay in each cell, though with a variety of timescales that prevent us from<br />
simply averaging different cells <strong>to</strong>gether.<br />
What if we have only a single cell? I will present our Monte Carlo Maximum Likelihood with<br />
Bayesian statistics approach that allows us <strong>to</strong> extract information (or “fit”) a pho<strong>to</strong>bleach decay<br />
for an individual cell <strong>and</strong> find out the number of initial GFP that we have while focussing on the<br />
convergence criterias needed during the simulation in order <strong>to</strong> explore enough parameter space <strong>to</strong><br />
reach convergence.<br />
Note: Even though the abstract involves biology terminology, the talk only involves mathematics<br />
<strong>and</strong> statistics with abosolutely no biology background required.
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 41<br />
Cooking Howard’s Curry With The Agda Programming Language<br />
Sean Hunt<br />
This talk will be an introduction <strong>to</strong> the Curry-Howard correspondance between proofs in formal<br />
logic systems <strong>and</strong> type checking in programming languages. This remarkable observation allows<br />
for veriation of proofs by way of checking that a computer program compiles. This is exploited by<br />
computer systems such as Coq <strong>and</strong> Agda <strong>to</strong> allow for formal veriation of proofs.<br />
The talk will include a brief explanation of the correspondance, but the main focus will be on<br />
taking advantage of the correspondance with the Agda programming language in order <strong>to</strong> make<br />
non-trivial proof. The limitations of this environment, both in terms of the limitations of what can<br />
be proved, as well as requirements for human interaction. The speaker hopes <strong>to</strong>, time permitting, be<br />
able demonstrate a proof of an interesting but relatively simple elementary theorem of mathematics.<br />
Required Background: none<br />
Derivative Free Optimization: An Investigation of Algorithms<br />
on Sample Functions<br />
Spencer Hunt<br />
From the dawn of time, it has been known that extremely powerful data can be found in the<br />
derivatives of any function one wishes <strong>to</strong> optimize. Many "st<strong>and</strong>ard" definitions of local minima,<br />
given by first-order necessary conditions, are in fact, for continuously differentiable functions, that<br />
the first-order derivatives are indeed zero. In a fantastical world, all functions would have easily<br />
attainable derivatives. But this is the Real World–seven strangers, picked <strong>to</strong> live in a house–<strong>and</strong><br />
not all functions provide reliable derivatives. Is is because of this, that the branch of derivative-free<br />
optimization was born. I will be discussing three basic derivative-free optimization techniques <strong>and</strong><br />
applying them <strong>to</strong> a number of sample functions. These functions are made <strong>to</strong> test the robustness of<br />
the algorithms. As well, they will highlight some of the problems that many mathematicians face<br />
in derivative-free optimization. Please join me in our exploration in<strong>to</strong> derivative-free optimization,<br />
a world of mystery <strong>and</strong> wonder.
42 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
On MDS Codes, the Main Conjecture, <strong>and</strong> the Partition Weight<br />
Enumera<strong>to</strong>r<br />
Svenja Huntemann<br />
Maximum Distance Separable (MDS) codes are those error-correction codes that have the largest<br />
possible minimum distance, which means that they can correct more errors than any other type of<br />
code. MDS codes have many applications in the industry <strong>and</strong> every-day life.<br />
One important area of research concerning this type of codes is finding an upper bound on<br />
the length n of the codewords given the alphabet size q <strong>and</strong> the dimension k. This long-st<strong>and</strong>ing<br />
problem is also important for combina<strong>to</strong>rial <strong>and</strong> experimental designs <strong>and</strong> in finite geometry.<br />
For linear MDS codes there has recently been a great advance <strong>to</strong>wards solving this problem <strong>and</strong><br />
proving the main conjecture <strong>to</strong> be true. The main conjecture states that the upper bound on n is<br />
q + 1, except for k = 3 or k = q − 1 <strong>and</strong> q even, where it is q + 2.<br />
For general, not necessarily linear, MDS codes very little is known about the upper bound. A<br />
summary of known upper bounds with an emphasis on bounds related <strong>to</strong> the main conjecture will<br />
be presented.<br />
A new technique for proving these upper bounds in the general case uses the partition weight enu-<br />
mera<strong>to</strong>r (PWE). The PWE for linear MDS codes has been introduced by El-Khamy <strong>and</strong> McEliece<br />
(2005), <strong>and</strong> their proof can be easily adjusted for general MDS codes. Several examples deriving<br />
upper bounds using the PWE <strong>to</strong>gether with other combina<strong>to</strong>rial techniques will be given.<br />
An Individual Based Model for Bear Movement<br />
Andrea Hyde<br />
The International Bear Association lists 6 of the 8 bear species world wide as endangered or<br />
threatened. Neither the American Black Bear or the Brown Bear are currently listed. However,<br />
with the expansion of <strong>to</strong>urism, <strong>and</strong> industry in<strong>to</strong> the back country, the increased rate of human bear<br />
interactions may change that. This project aims <strong>to</strong> underst<strong>and</strong> the effect that different Human-<br />
Bear Management strategies have on the movement patterns <strong>and</strong> rates of human bear interactions<br />
in Communities. I will present a novel individual-based model for bear movement in which the<br />
displacement of a bear from one habitat patch <strong>to</strong> another follows a probability function. It is not<br />
known exactly what this function should depend upon, <strong>and</strong> so our mathematical approach is helping<br />
<strong>to</strong> elucidate the motivating fac<strong>to</strong>rs for bear movement, their relative importance, <strong>and</strong> the dispersal<br />
patterns that result.<br />
Preliminary investigations show that including the location of food sources <strong>and</strong> of Human-Bear<br />
Interactions (HBI) is sufficient <strong>to</strong> create realistic movement patterns for an individual bear.
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 43<br />
An Introduction <strong>to</strong> Topology<br />
Neal Jackett<br />
Topology is the study of how properties of the domain <strong>and</strong> range affect the behaviour of a<br />
continuous mapping. We will explore the concept of <strong>to</strong>pological spaces <strong>and</strong> subspaces <strong>and</strong> the<br />
continuity inherent in them. We will also discuss connectivity <strong>and</strong> compactness of <strong>to</strong>pological<br />
spaces <strong>and</strong> look at familiar examples.<br />
A Simple Proof of the Jordan Curve Theorem<br />
Ifaz Kabir<br />
The Jordan Curve Theorem states an obvious, but hard <strong>to</strong> prove fact: that a simple closed curve<br />
divides the plane in<strong>to</strong> two components, one bounded <strong>and</strong> one unbounded. In this talk I will attempt<br />
<strong>to</strong> give a simple proof of the Jordan Curve Theorem assuming some easy <strong>to</strong> prove ‘hammers’ such<br />
as the Brouwer Fixed Point Theorem.<br />
Representations <strong>and</strong> Duality with a View <strong>to</strong>wards Number Theory<br />
Jamie Klassen<br />
I will provide a quick, flashy <strong>and</strong> results-oriented approach <strong>to</strong> representation theory (focusing<br />
on finite groups <strong>and</strong> providing analogies <strong>to</strong> linear algebraic groups when necessary) <strong>and</strong> discuss<br />
some elementary results concerning Kronecker coefficients <strong>and</strong> Schur-Weyl duality as well as some<br />
indications of their broader consequences in the realm of au<strong>to</strong>morphic forms <strong>and</strong> modern number<br />
theory. Students will need some familiarity with the concepts of linear algebra <strong>and</strong> basic abstract<br />
algebra. As an example, you should underst<strong>and</strong> what GLn means <strong>and</strong> what Sd the symmetric<br />
group is, ideally as well as the significance of such <strong>to</strong>pics as number fields <strong>and</strong> Galois theory.<br />
Flows, Branching Numbers, <strong>and</strong> Percolation on Trees<br />
Jason Klusowski<br />
Let T be a locally finite tree <strong>and</strong> fix p ∈ [0, 1]. For each vertex v of T , r<strong>and</strong>omly declare v <strong>to</strong> be<br />
open with probability p. Otherwise v will be closed with probability 1 − p. Make the choice of the<br />
state of each vertex independent of the state of every other vertex of T . A path P in T is open if<br />
all the vertices of P are open in T .
44 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
A natural question <strong>to</strong> ask is if there exists a critical probability in which such open paths exist<br />
in T with positive probability, <strong>and</strong> if so, how it might relate <strong>to</strong> Gal<strong>to</strong>n-Watson branching processes<br />
conditioned on survival? I will answer this question by introducing the concepts of a flow <strong>and</strong> a<br />
branching number along with some of their elementary properties <strong>and</strong> a couple of examples.<br />
An Introduction <strong>to</strong> Machine Learning for Text Classification<br />
Michelle Kovesi<br />
How can a computer be programmed <strong>to</strong> classify inputs in<strong>to</strong> various categories? The answer,<br />
often, is <strong>to</strong> use machine learning. Machine learning is a branch of artificial intelligence that is<br />
concerned with making computers evolve in response <strong>to</strong> input. This talk will give a basic introduc-<br />
tion <strong>to</strong> the <strong>to</strong>pic of machine learning for text classification. It will include information on how <strong>to</strong><br />
prepare text documents for classification, as well as how the classification algorithms actually work.<br />
As an example, we will look at a basic classification algorithm called the Perceptron. Finally, I will<br />
present a new multi-lingual classifier that I implemented last summer.<br />
Required Knowledge: none<br />
Proof of Brouwer Fixed Point Theorem, using Sperner’s<br />
Lemma<br />
Jean Lagacé<br />
Brouwer Fixed Point Theorem states that any continuous mapping from a compact convex<br />
subset of an Euclidean space in<strong>to</strong> itself has a ed point, i.e. a point such that f(x) = x. While this<br />
theorem is considered <strong>to</strong> be one of the key theorems concerning the <strong>to</strong>pology of Euclidian spaces,<br />
it has applications in many mathematical lds, ranging from differential equations <strong>to</strong> game theory.<br />
As such, a variety of proofs arise with arguments coming from a wide range of lds. Here, a graph<br />
theory result, Sperner Lemma, will be used <strong>to</strong> prove that the Brouwer Fixed Point Theorem is true<br />
for any simplex in R n , <strong>and</strong>, since the ed point property is conserved by homeomorphisms, true for<br />
any compact convex subset of R n .
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 45<br />
Brain, Dynamical Systems <strong>and</strong> Fun!<br />
Jean-Sébastien Lévesque<br />
Dans plusieurs régisons du cerveau, les neurones s’organisent en petits groupes capables de<br />
produire des oscillations. Ces oscillateurs neuronaux interagissent entre eux par de faibles connex-<br />
ions et peuvent précenter divers phénomènes de synchronisation. Dans cet exposé, il sera ques-<br />
tion d’oscillateurs faiblement couplés et principalement de différentes dynamiques (comportement<br />
péiodique, quasi-péiodique, synchronisation) observables sur un <strong>to</strong>re, l’espace de phase naturelle-<br />
ment associé à un système de deux oscillateurs couplés.<br />
Required Background: At least one eye, <strong>to</strong> see great pictures <strong>and</strong> cool videos!<br />
The Roots of Flow <strong>and</strong> Chromatic Polynomials<br />
Richard Leyl<strong>and</strong><br />
Using graph flows one can model many different phenomena such as electricity or networks. So<br />
it is important <strong>to</strong> know if a graph has a k-flow. The flow polynomial ΦG(x) tells us the number of<br />
such flows. It turns out the flow polynomial is related <strong>to</strong> the chromatic polynomial of the planar<br />
dual χG∗(x), which tells us the number of k colorings. In a paper by Sokal, he shows that the roots<br />
of chromatic polynomials are dense in the complex plane. I will discuss this result <strong>and</strong> what we<br />
results we hope <strong>to</strong> obtain with flow polynomials, along with some conjecture regarding the roots of<br />
flow polynomials.<br />
Combina<strong>to</strong>rial Designs <strong>and</strong> Block-Intersections Graphs<br />
Robert Luther<br />
A combina<strong>to</strong>rial design D is a pair (V, B) where V is a set of distinct points <strong>and</strong> B is a set of<br />
subsets of V called blocks.<br />
A pairwise balanced design P BD(v, K, λ) is a design D = (V, B) where v = |V | <strong>and</strong> each pair of<br />
points of V occurs in exactly λ blocks of B. In addition, the cardinality of each block of B must be<br />
an element of K. If K should consist of a single element, say K = {k}, then the design is called a<br />
balanced incomplete block design BIBD(v, k, λ). In addition <strong>to</strong> the constant block size in a BIBD,<br />
there is a fifth parameter r called the replication number which is the number of times any one<br />
point of V occurs in the blocks of B.
46 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
The block-intersection graph of a design D = (V, B) is the graph GD having the block set B as<br />
its vertex set <strong>and</strong> such that two vertices B1 <strong>and</strong> B2 are adjacent if <strong>and</strong> only if (B1 ∩ B2) �= ∅.<br />
A cycle in a graph G is a closed path in G such that no vertex is repeated more than once.<br />
A cycle that contains every vertex in a graph is called a Hamil<strong>to</strong>n cycle <strong>and</strong> if a graph G has a<br />
Hamil<strong>to</strong>n cycle, then G is called Hamil<strong>to</strong>nian. A graph G is called pancyclic if G has a cycle of<br />
every possible length, from a 3-cycle <strong>to</strong> a Hamil<strong>to</strong>n cycle.<br />
We discuss some known results about cycles in block-intersection graphs of BIBDs <strong>and</strong> of<br />
P BDs as well as some open questions regarding cycles in these block-intersection graphs.<br />
Using Symmetry Groups <strong>to</strong> Solve Partial Differential Equations<br />
Keenan Lyon<br />
Many of the useful properties of symmetry groups on partial differential equations (PDEs) arise<br />
from the fact that they are Lie groups, which are differentiable manifolds endowed with a group<br />
structure. The smooth manifold part of the Lie group allows one <strong>to</strong> continuously vary the elements<br />
in the Lie group. The idea of using group theory <strong>to</strong> solve ODEs first originated at the turn of the<br />
century by Sophus Lie. Although he did not finish his work, the applications of his Lie groups <strong>and</strong><br />
Lie algebras are ever present in many fields of math, <strong>and</strong> the technique of using symmetry groups<br />
<strong>to</strong> find PDE solutions is still a matter of much research.<br />
PDEs model systems that depend on several variables. For example, the schrodinger equation is<br />
a PDE where the solutions depend on both the position of a particle <strong>and</strong> the time of the system; it<br />
is the fundamental of non-relativistic quantum mechanics. The heat equation is another example,<br />
<strong>and</strong> it models the distribution of heat over time given some initial condition, <strong>and</strong> it can also be used<br />
<strong>to</strong> model particle diffusion. These two examples show the various applications that PDEs have in<br />
describing natural processes.<br />
The spirit of finding symmetry groups of PDEs is that one solution, via some group element of<br />
the symmetry group, can be transformed in<strong>to</strong> another solution. Since the groups are Lie groups, this<br />
implies a family of infinite solutions which can be created from just one solution. The motivation<br />
behind this talk is <strong>to</strong> outline the basic algorithm first created by Lie <strong>to</strong> find solutions. On the<br />
way <strong>to</strong> applying the algorithm, <strong>and</strong> extensive look in<strong>to</strong> Lie groups, vec<strong>to</strong>r fields, group actions <strong>and</strong><br />
<strong>to</strong>pology will be aided by examples.
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 47<br />
Fundamental Theorem of Calculus for Lebesgue Integration<br />
Richard Mack<br />
The Fundamental Theorem of Calculus is one of the core results in analysis. However, in its<br />
st<strong>and</strong>ard form taught in beginning calculus/analysis courses, it applies only when the function has<br />
continuous derivatives, which is a very small class of functions. In my talk, I will be discussing a<br />
generalization of the Fundamental Theorem of Calculus <strong>to</strong> the Lebesgue integral, <strong>and</strong> the proof in<br />
the context of measure theory, based on Lebesgue-Radon-Nicodym theorem <strong>and</strong> absolute continuity.<br />
This talk will be aimed <strong>to</strong>ward an audience with some exposure <strong>to</strong> measure theory.<br />
Introduction aux méthodes de Schwarz<br />
Dominique Maheux<br />
Plusieurs méthodes de résolution matricelle sont à notre disposition. D’une part, on connaît la<br />
méthode de la matrice inverse ou la décomposition LU, qui sont des méthodes directes. D’autre<br />
part, il existe aussi certaines méthodes itératives qui permettent d’approximer la solution désirée.<br />
Toutefois, les méthodes directes sont souvent trop coûteuses et les méthodes itératives ne sont pas<br />
<strong>to</strong>ujours très robustes. Nous allons proposer un compromis entre ces deux types de méthodes, soit<br />
la décomposition de domaine. Nous présenterons quelques méthodes de Schwarz en expliquant les<br />
avantages et les inconvénients de ces méthodes.<br />
Il s’agit d’une présentation très simple qui ne nécessite que quelques notions de base i.e. savoir<br />
ce qu’est une équation et une dérivée!<br />
Structure of Neural Networks<br />
Isaiah M<strong>and</strong>ryk<br />
Artificial neural networks are computational models inspired by the way neurons pass informa-<br />
tion via synapses in the brain. They are effective for modelling complex nonlinear relationships<br />
between an input <strong>and</strong> output set of data vec<strong>to</strong>rs where there is little or no a priori information<br />
about the relationships, <strong>and</strong> are also very helpful for discovering patterns in data. The connec-<br />
tivity between nodes in the network is often represented by a graph, with neurons as nodes <strong>and</strong><br />
synapses as edges. The structure of this graph can have enormous implications on the performance<br />
of the neural network. This talk focuses on the different types of structures typically used in neural<br />
network implementations <strong>and</strong> the effects the different architectures have on the network. These<br />
include differences in the capability of the network <strong>to</strong> generalize the learned information <strong>to</strong> apply
48 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
<strong>to</strong> new data, the number of mathematical operations (<strong>and</strong> thus the amount of time) required <strong>to</strong><br />
train the network, <strong>and</strong> the capacity for the network <strong>to</strong> approximate arbitrary functions.<br />
Introduction <strong>to</strong> Additive Frieze Patterns<br />
Jean-François Marceau<br />
Additive Frieze Patterns are pure combina<strong>to</strong>rial objects that were developed by G.C. Shephard<br />
in 1976. Even if they are now 36 years old, just few mathematicians studied them so they are not<br />
well known. In this talk, I will present the results I got from my research on the subject during<br />
summer 2011 (see arXiv 1205.5213).<br />
Weyl’s Theorem<br />
Joanie Martineau<br />
Weyl’s theorem is the first interesting result found in spectral geometry. This theorem gives<br />
us an asymp<strong>to</strong>tic expression for the number of eigenvalues of the Laplacian opera<strong>to</strong>r for bounded<br />
domains in Euclidean space. This talk will introduce the basic concepts of spectral geometry <strong>and</strong><br />
prove intuitively Weyl’s theorem.<br />
Dirichlet Series <strong>and</strong> Arithmetic Functions<br />
Kevin Mather<br />
We will discuss basic detions <strong>and</strong> convergence of Dirichlet Series, construction of Dirichlet Series<br />
by Arithmetic Functions, fac<strong>to</strong>rization of Dirichlet Series, <strong>and</strong> the similarities of Dirichlet Series <strong>to</strong><br />
power series<br />
The S<strong>to</strong>ry of Srinivasa Ramanujan<br />
Arthur Mehta<br />
The talk will be split in<strong>to</strong> segments. The first segment will consist of a brief telling of the one<br />
of the most romantic s<strong>to</strong>ries in the his<strong>to</strong>ry of mathematics: the s<strong>to</strong>ry of Srinivasa Ramanujan.<br />
Ramanujan was a self-taught Indian mathematician who was born in<strong>to</strong> poverty. After years of<br />
obscurity his talent was finally recognized by G.H Hardy, a prominent mathematician at Trinity
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 49<br />
College, Cambridge. The discovery of Ramanjuan eventually resulted with him traveling <strong>to</strong> Engl<strong>and</strong><br />
<strong>to</strong> work alongside Hardy. This led <strong>to</strong> one of the most productive mathematical partnerships of the<br />
20th century, <strong>and</strong> resulted in works contributing <strong>to</strong> a wide variety of areas, including Number theory,<br />
Analytic Combina<strong>to</strong>rics, Infinite Fractions <strong>and</strong> Infinite Series. This segment will be followed by a<br />
segment devoted <strong>to</strong> examining a select set of works completed by Ramanujan. These works will<br />
include a look at Ramanujan work on Highly Composite Numbers: his contribution <strong>to</strong> determining<br />
the number of partitions of a given number. Lastly we will examine a host of intriguing identities,<br />
infinite series <strong>and</strong> infinite fractions produced by Ramanujan.<br />
Required background: none<br />
From Differential Equations <strong>to</strong> Diphtheria: the Mathematics<br />
of Infectiouse Disease Spread<br />
Irena Papst - English talk with Bilingual slides<br />
In recent years, mathematical modeling has become an important <strong>to</strong>ol in epidemiology. Math-<br />
ematicians are able <strong>to</strong> create models of infectious disease spread which can be used predict the<br />
outcome of an outbreak in different populations, as well as the effectiveness of various control<br />
strategies, all without risking the public’s safety. This <strong>to</strong>ol enables public health agencies <strong>to</strong> make<br />
well-founded decisions in high-risk situations.<br />
In this talk, we will introduce the concept of mathematical modeling <strong>and</strong> discuss what makes<br />
a good model. We will focus on the application <strong>to</strong> epidemiology <strong>and</strong> consider one of the simplest<br />
epidemiological models, the SIR model, in order <strong>to</strong> draw important conclusions from it. However,<br />
models are not perfect; they must be set up, adjusted, <strong>and</strong> interpreted carefully, while bring mindful<br />
of observed data. We will analyze the simple SIR model in the context of childhood diseases such<br />
as measles, mumps, <strong>and</strong> rubella, <strong>and</strong> adjust it accordingly <strong>to</strong> make other important conclusions<br />
about the dynamics of these infectious diseases.<br />
Recommended background: First year calculus, some experience with ordinary differential equa-<br />
tions.
50 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
Diophantine Approximations<br />
Hongyoul (Mike) Park<br />
The field of Diophantine approximations is the study of the approximation of real numbers by<br />
rational numbers.<br />
First, we need <strong>to</strong> make sure that the problem of rational approximation is well formulated. Let<br />
α be some real number which we would like <strong>to</strong> approximate by rational numbers. We know that<br />
rational numbers Q form a dense set on the real line R; this means that we can always find a<br />
rational number arbitrarily close <strong>to</strong> α. Moreover, for any ε > 0, there are infinitely many rationals<br />
a/b ∈ Q satisfying |α − a/b| < ε. Thus, we need <strong>to</strong> adjust the problem.<br />
One possible approach is <strong>to</strong> make ε depend on denomina<strong>to</strong>rs of rational approximations. Specif-<br />
ically, let ε(b) = 1/b k where k is some positive integer. Are there rational numbers which satisfy<br />
|α − a/b| < ε(b)? How many rationals (finitely many or infinitely many) satisfy this inequality?<br />
As it turns out, the answers <strong>to</strong> these questions depend not only on the value of k, but also on the<br />
intrinsic properties of the number we seek <strong>to</strong> approximate! For instance, there are famous theorems<br />
by Liouville <strong>and</strong> Roth which assert that algebraic numbers cannot be approximated “<strong>to</strong>o well" by<br />
rationals.<br />
In my talk, I will discuss how algebraic numbers behave with respect <strong>to</strong> Diophantine approxi-<br />
mations. I will construct examples of numbers which have very good rational approximations <strong>and</strong>,<br />
therefore, cannot be algebraic. I will also explain how <strong>to</strong> find good rational approximations using<br />
the theory of continued fractions.<br />
A Brief His<strong>to</strong>ry of Women in Mathematics<br />
Crystal Parras<br />
This presentation was inspired by my first encounter reading about a female mathematician,<br />
Sophie Germain. The lengths at which she went <strong>to</strong> study mathematics against her parents’ wishes<br />
fascinated me. This lead me <strong>to</strong> explore further s<strong>to</strong>ries of other women in mathematics: the contri-<br />
bution they made, the people they interacted with, the lives they lived. This presentation will give<br />
a brief overview of the lives of some female mathematicians, whose s<strong>to</strong>ries have caught my eye.<br />
Probability <strong>and</strong> Measure<br />
Laurent Pelletier<br />
In this talk, we will try <strong>to</strong> motivate <strong>and</strong> introduce the concepts of measure theory by proba-<br />
bilistic means. The concept of a measure is fundamental in probability theory. On the other h<strong>and</strong>,
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 51<br />
probabilities give an interesting meaning <strong>to</strong> the usual objects of measure theory. Subsets become<br />
events, σ-algebras talk about independence....<br />
Required Background: You don’t need <strong>to</strong> know about measure theory, a basic probability course<br />
will be enough.<br />
Investigating Orthogonal Latin Squares Using Universal Algebra<br />
David Peterson<br />
Latin squares are simple mathematical objects that are familiar <strong>to</strong> anyone who has solved a<br />
Sudoku puzzle – a special type of Latin square. Basically a Latin square is a square matrix of<br />
entries from some set S such that every element of S occurs in every column <strong>and</strong> every row. We<br />
will be investigating pairs of orthogonal Latin squares; that is, a pair of Latin squares A, B with<br />
entries from some set S such that for every (a, b) ∈ S 2 there is a unique pair of row i <strong>and</strong> column<br />
j such that (aij, bij) = (a, b). We will explore these structures by converting them <strong>to</strong> algebraic<br />
structures, thereby allowing us <strong>to</strong> take advantage algebraic techniques (as well as providing a good<br />
excuse <strong>to</strong> do some neat algebra). In particular, we will refute a conjecture by Euler stating that it<br />
is impossible <strong>to</strong> find a pair of orthogonal Latin squares if |S| ≡ 2 (mod 4).<br />
Required Background: Some familiarity with basic abstract algebra, especially group theory,<br />
is helpful but not strictly necessary as this talk aims <strong>to</strong> be reasonably self contained. Everyone is<br />
welcome <strong>and</strong> should get something out of the talk.<br />
Math <strong>and</strong> Art: the math behind the beauty<br />
Tara Petrie<br />
Many people are skeptical when they hear that math <strong>and</strong> art are interwoven throughout his<strong>to</strong>ry<br />
<strong>and</strong> that in some universities you can get a math degree through the faculty of arts; but the truth<br />
is that although they seem like very different subjects, math <strong>and</strong> art have influenced <strong>and</strong> grown<br />
from each other since their creation. My talk focuses on the influence of mathematics in art <strong>and</strong><br />
architecture, particularly concerning the golden ratio <strong>and</strong> certain geometric shapes <strong>and</strong> patterns. I<br />
was very fortunate <strong>to</strong> spend two weeks of May studying in Italy; the vast art <strong>and</strong> architecture in<br />
that area inspired me <strong>to</strong> learn more about the math behind the beauty.<br />
Because the connections between math <strong>and</strong> art are so numerous, I have decided <strong>to</strong> concentrate<br />
mainly on Ancient times <strong>and</strong> the Renaissance as well as some modern mathematical art, with my
52 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
presentation set up as a timeline. I start by explaining the Golden Ratio, geometric shapes designed<br />
according <strong>to</strong> the Golden Ratio, <strong>and</strong> its influence on the Great Pyramids <strong>and</strong> the Parthenon. I<br />
then discuss ancient artist <strong>and</strong> mathematician Polyklei<strong>to</strong>s <strong>and</strong> his Canon. Next I move <strong>to</strong> the<br />
Renaissance, focusing on the development of perspective including Piero della Francesca logical art<br />
in his De Prospectiva Pingendi as well as the various mathematical influences within Leonardo da<br />
Vinci work. Lastly, I give a quick discussion on more modern mathematical art from M.C. Escher,<br />
John Robinson, <strong>and</strong> various others.<br />
I believe this is a good <strong>to</strong>pic because no matter at which level an undergraduate student st<strong>and</strong>s,<br />
he or she will be able <strong>to</strong> underst<strong>and</strong> <strong>and</strong> find value in this discussion. With particular emphasis on<br />
geometry <strong>and</strong> perspective <strong>and</strong> using specific examples of art <strong>and</strong> architecture throughout his<strong>to</strong>ry,<br />
I hope <strong>to</strong> ignite in my audience the same fascination I have with two interconnected subjects that<br />
are commonly viewed as polar opposites.<br />
On the Existence of Double Arithmetic Progressions<br />
Andrew Poelstra<br />
Van der Waerden’s Theorem states that for any number of colors r, <strong>and</strong> any length k, every<br />
r-coloring of the natural numbers must contain a monochromatic k-term arithmetic progression (a<br />
sequence x1, x2, . . . , xk with constant gap between consecutive entries.)<br />
We extend this idea <strong>to</strong> double k-term arithmetic progressions: sets xi1 , xi2 , . . . , xik which have<br />
constant gap between consecutive entries, <strong>and</strong> constant gap between consecutive indices.<br />
We ask whether every r-coloring of the natural numbers must contain a k-term arithmetic<br />
progression, present computational evidence <strong>to</strong> suggest that the answer is (in general) no, <strong>and</strong> show<br />
that this question is equivalent <strong>to</strong> one about infinite words on finite alphabets.<br />
A Topological Proof of the Infinitude of Primes<br />
Alex Provost<br />
It is well-known that there is an infinite number of primes; Euclid offered the first known proof<br />
of that statement circa 300 BC.<br />
In this talk I will give a beautiful proof of the infinitude of primes using elementary notions of<br />
point-set <strong>to</strong>pology. This modern proof was discovered in 1955 by mathematician Furstenberg. No<br />
anterior knowledge of <strong>to</strong>pology is assumed; the basic concepts (<strong>to</strong>pological space, closed <strong>and</strong> open<br />
sets, base) will be explained along the way.
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 53<br />
VC Dimension <strong>and</strong> Density: Connections between Computational<br />
Learning Theory <strong>and</strong> Model Theory<br />
Nigel Pynn-Coates<br />
In this talk we will introduce the notions of Vapnik-Chervonenkis dimension <strong>and</strong> density de-<br />
veloped in computational learning theory. These notions are important because they determine<br />
whether a concept is uniformly learnable, a key question in computational learning theory. Along<br />
the way, we will also consider some st<strong>and</strong>ard mathematical examples <strong>to</strong> help clarify these ideas.<br />
Model theory is a branch of mathematical logic seemingly unconnected <strong>to</strong> computational learning<br />
theory. In fact, there is an interesting connection <strong>and</strong> we will see how a model-theoretic perspective<br />
leads <strong>to</strong> new results about VC theory. In particular, it is used <strong>to</strong> prove uniform bounds on VC<br />
density in different structures. Finally, we will consider a theorem from computational learning<br />
theory (translated in<strong>to</strong> probability theory) <strong>and</strong> discuss how we can use the theorem <strong>to</strong> guess at the<br />
VC dimension or density of families of sets.<br />
Recommended background knowledge: some elementary logic would be helpful (e.g. formulas,<br />
realisations) but is not required <strong>to</strong> underst<strong>and</strong> most of the talk.<br />
Causal Inference <strong>and</strong> Bayesian Propensity Score Adjustment<br />
Methods<br />
Léo Raymond-Belzile<br />
Often times, in the context of policy analysis or medical research, one is interested in establishing<br />
causal relationship between variables, for example the effect of legislation on individual’s behaviour<br />
or the impact of a drug on survival. The purpose of the talk is <strong>to</strong> introduce the Rubin Causal<br />
Model framework along with the various challenges faced in the area of causal inference. I will<br />
introduce some basic statistical notions, as well as confounding, propensity score adjustment (PSA)<br />
<strong>and</strong> ways <strong>to</strong> adjust for uncertainty in the context of missing data problem. The incapacity of the<br />
PSA method <strong>to</strong> incorporate uncertainty arising from the evaluation of the propensity score model<br />
justifies some recent literature on Bayesian PSA which will be discussed. A first course in statistics<br />
is assumed.
54 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
Critical Issues in Statistical <strong>and</strong> Biological Interpretation<br />
Jeremy Recoskie<br />
Within the field of medicine, there is a constant written dialogue through various medical<br />
journals, papers, <strong>and</strong> reports. Professionals within the academic disciplines of medicine, health,<br />
biology, statistics, <strong>and</strong> mathematics are primary contribu<strong>to</strong>rs <strong>to</strong> these texts. Due <strong>to</strong> the complexity<br />
involving many disciplines, authors, <strong>and</strong> re- searchers, there is a clear need for a common language<br />
of dissemination so that the results of these texts may be more easily interpreted across multiple<br />
disciplines.<br />
In a recent survey of the 2009 H1N1 p<strong>and</strong>emic literature, there were several in- stances where<br />
semantic <strong>and</strong> statistical misinterpretation or miscommunication arose. These examples could be of<br />
use <strong>to</strong> interdisciplinary groups or researchers in the field of medicine.<br />
The focus of this talk is on the mathematical <strong>and</strong> statistical issues realized through the literature<br />
reviewed, however some semantic issues will also be mentioned. Included will be examples of<br />
how improper use of hypothesis testing, density fitting, citations <strong>and</strong> terminology contribute <strong>to</strong> a<br />
decreased quality of research texts. Discussion of all aspects is key <strong>to</strong> the goal of a more precise<br />
underst<strong>and</strong>ing of the many texts that comprise medical research.<br />
Simplicial k-Complexes <strong>and</strong> Packings: Touching (k + 1)-tuples of<br />
Congruent Balls in 3-space<br />
Samuel Reid<br />
By generalizing the problem in combina<strong>to</strong>rial geometry of determining the maximum number<br />
of <strong>to</strong>uching unit balls in a packing of n unit balls, we define a class of problems captured by the ∆-<br />
function, ∆k d (n), which determines the maximum number of <strong>to</strong>uching (k+1)-tuples of unit d-balls in<br />
a packing of n unit balls in Ed . The case of k = 1 was studied by Heiko Harborth in E2 (1974) <strong>and</strong><br />
Károly Bezdek in E 3 (2010), where Harborth proved the precise result of ∆ 1 2(n) = ⌊3n − √ 12n − 3⌋<br />
<strong>and</strong> Bezdek gave an upper bound of ∆ 1 3(n) < 6n−0.695n 2/3 , provided n ≥ 2. By applying Bezdek’s<br />
upper bound on ∆ 1 3(n) <strong>to</strong> the case of pairwise <strong>to</strong>uching 4-tuples (quadruplets) of spheres in E 3 ,<br />
<strong>and</strong> using a simple combina<strong>to</strong>rial argument, we prove an initial bound of ∆ 3 3(n) < 4n − 0.463n 2/3 .<br />
To improve this upper bound independent of the bounds for k = 1, we construct an approach<br />
<strong>to</strong> finding upper bounds on ∆k d (n), where k ≥ 2, by observing that ∆k d (n) equivalently describes<br />
the maximum cardinality of a simplicial k-complex K in Ed determined by an n-element point set<br />
in E d , where the minimum distance between points is of twice the radius of the unit d-ball. By<br />
proving two key lemmas, that (1) at most four tetrahedra can share an edge in K, <strong>and</strong> (2) at most<br />
twelve tetrahedra can share a vertex in K, we prove that ∆ 3 3(n) ≤ 12n/4 = 3n. We propose a
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 55<br />
research program <strong>to</strong> determine the behaviour of the ∆-function in non-Euclidean geometries, such<br />
as spherical <strong>and</strong> hyperbolic geometry, as well as in higher dimensions.<br />
Lost in Intervention: Conditioning of Spectral Collocation<br />
Methods<br />
Sarah Reimer<br />
Spectral collocation methods are used <strong>to</strong> solve boundary value problems for ordinary differen-<br />
tial equations with narrow boundary layers. The numerical results are very accurate, despite the<br />
sometimes severe ill-conditioning of the system matrices arising. Equations with zero boundary<br />
conditions do not amplify perturbations, but equations with nonzero boundary conditions do. By<br />
solving an equation with inhomogeneous boundary conditions in two steps we maintain accuracy<br />
<strong>and</strong> increase the robustness of our method.<br />
Pattern Subgroups of GLn(F)<br />
Larissa Richards<br />
This talk assumes knowledge from an Introduc<strong>to</strong>ry Course in Abstract Algebra/Group Theory<br />
<strong>and</strong> is built from a chapter of G.D. James’ Representations of General Linear Groups with the<br />
help of Professor Fern<strong>and</strong>o Szchetman. The theory of representation of the symmetric groups<br />
is extremely elegant <strong>and</strong> can be used in several ways <strong>to</strong> find representations of other groups. In<br />
addition, their theory has applications in fields such as quantum mechanics <strong>and</strong> polynomial identity<br />
algebras. There is a close connection between the representations of the symmetric groups over a<br />
field F <strong>and</strong> the representations of GLn(F) over the same field. The finite general linear group is<br />
associated <strong>to</strong> a finite subset of a real vec<strong>to</strong>r space with certain combina<strong>to</strong>rial properties known<br />
as its root system. The classification of GLn(F) reduces <strong>to</strong> the classification of root systems <strong>and</strong><br />
the structure of any of these groups can be obtained from properties of its root system. We will<br />
introduce the pattern (root) subgroups of GLn(F) <strong>and</strong> prove an easy result which is of fundamental<br />
importance in the representations of GLn(F). This will lead us <strong>to</strong> two interesting open problems.
56 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
Introduction <strong>to</strong> Estimation<br />
William Ruth<br />
Making predictions is one of the most fascinating problems in statistics. It allows for everything<br />
from engineering buildings <strong>to</strong> deciding the risk of heart attacks in cardiac patients. I this talk, I<br />
will introduce a popular framework for predictions <strong>and</strong> 2 models that have been proposed <strong>to</strong> h<strong>and</strong>le<br />
it.<br />
The framework being discussed is called regression, in which a response variable (dependent<br />
variable) is predicted based on knowledge of some set of predic<strong>to</strong>r variables (independent variables).<br />
The first model, known as linear regression, s the more well known of the two models <strong>and</strong> will share<br />
the first 1/3 of the talk with setting up the framework. This model consists of expressing the<br />
response variable as a linear combinations of the predic<strong>to</strong>r variables <strong>and</strong> choosing the ’best’ such<br />
linear combination. The second model is called a regression tree <strong>and</strong> is only usually taught i<br />
graduate courses on data mining. This model will also receive about 1/3 of the talk <strong>and</strong> consists<br />
of partitioning the data then estimating each part ion separately. The final third of the talk will<br />
be split between a few <strong>to</strong>pics related <strong>to</strong> the two models. This will included a discussion of how <strong>to</strong><br />
evaluate a model, a comparison of the strengths <strong>and</strong> weaknesses of each of the models discussed,<br />
<strong>and</strong> a brief introduction <strong>to</strong> a few procedures that extend the basic regression tree structure.<br />
This will be an elementary presentation that assumes almost no background in statistics (if you<br />
know what a mean is then you’re good). As such, it will be more of an overview of a few areas<br />
than in in-depth analysis of one <strong>to</strong>pic. In conclusion, this talk is a good opportunity <strong>to</strong> get an<br />
introduction <strong>to</strong> a fascinating <strong>and</strong> widely applicable area in statistics.<br />
As Easy as A, B, C<br />
Philip Ryan<br />
This talk introduces the ABC Conjecture in number theory, also known as the Oesterle-Masser<br />
Conjecture. If A, B, <strong>and</strong> C are natural numbers with no common fac<strong>to</strong>rs, with A + B = C,<br />
when is it possible that C is larger than the product of the prime fac<strong>to</strong>rs of ABC (that is, the<br />
largest square-free fac<strong>to</strong>r of ABC)? The conjecture claims "very rarely," <strong>and</strong> if true, it provides an<br />
incredibly powerful <strong>to</strong>ol which can be applied <strong>to</strong> a deep well of number theory, including Fermat’s<br />
Last Theorem <strong>and</strong> the Erdos-Mullin-Walsh conjecture on triplets of powerful numbers, as well as<br />
a host of other results <strong>and</strong> conjectures. I will explain the conjecture in full <strong>and</strong> work through an<br />
example of its use.<br />
Required background: Basic arithmetic
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 57<br />
Continuous Model Theory <strong>and</strong> von Neumann Algebras<br />
Nigel Sequeira<br />
In my talk, I will introduce the <strong>to</strong>pic of my summer research project: von Neumann algebras<br />
<strong>and</strong> some modern model theoretic approaches <strong>to</strong> their study. Basics ideas from opera<strong>to</strong>r theory<br />
<strong>and</strong>, more specifically, from the theory of von Neumann algebras, will be discussed. In particular,<br />
we will look at the opera<strong>to</strong>r-theoretic methods <strong>and</strong> constructions necessary <strong>to</strong> discuss aspects of<br />
the classification of type II fac<strong>to</strong>rs; emphasis will be put on the type III fac<strong>to</strong>rs, or tracial von Neu-<br />
mann algebras with trivial centres. Additionally, I will talk about some applications of continuous<br />
first-order logic in the context of von Neumann algebras, which will allow us <strong>to</strong> examine some of<br />
the current research <strong>and</strong> results from the intersection of opera<strong>to</strong>r theory <strong>and</strong> model theory.<br />
Assumed knowledge: A good course in linear algebra, basic logic <strong>and</strong> analysis. Basic <strong>to</strong>pology<br />
<strong>and</strong> more analysis is a plus, but not required. The required opera<strong>to</strong>r theory <strong>and</strong> model theory will<br />
be introduced as needed.<br />
Euclid’s Elements <strong>and</strong> Pythagoras’ Theorem<br />
Nicolas Simard<br />
This talk is divided in<strong>to</strong> two parts. In the first part, I will present some important facts (that<br />
all mathematicians should know) about Euclid’s elements <strong>and</strong> Pythagoras’ theorem. I will then<br />
explain the first book in more details, particularly the first rigorous proof of the Pythagorean<br />
theorem that Euclid elaborated. In the second part, it will be your turn <strong>to</strong> talk! Indeed, those who<br />
wish may share their knowledge by presenting, in than 150 seconds, a proof of the Pythagorean<br />
theorem. Try <strong>to</strong> find the most elegant, simple, <strong>and</strong> original proof! But do not forget, I’ve got the<br />
one from Euclid!<br />
Representations of Harmonic Donuts<br />
Michael Snarski<br />
What do a donut, real matrices with determinant one <strong>and</strong> the integers have <strong>to</strong> do with each<br />
other? What is the relationship between triangles, three letters, a 6-vertex directed graph – <strong>and</strong><br />
how can one "represent" this relationship? What do R/Z, 2×2 orthogonal matrices <strong>and</strong> eigenspaces<br />
of the Laplacian ∆f = d2 f<br />
dx 2 have in common?
58 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
As undergraduates, there are many fascinating connections between different fields of mathemat-<br />
ics we have yet <strong>to</strong> explore. This will be an example-based, picture-motivated chalk-talk which hopes<br />
<strong>to</strong> give a glimpse of some big ideas in math <strong>and</strong> give you an idea of what certain “buzz” words mean.<br />
Prerequisites include linear algebra (eigenstuff) <strong>and</strong> a first course in abstract algebra (familiarity<br />
with group structure).<br />
Achieving All Radio Numbers<br />
Benjmain(Ben) Sokolowsky<br />
For a connected graph G, a radio labelling is a function c : V (G) → Z + such that for every pair<br />
of vertices (u, v) in V (G), the radio condition is satisfied:<br />
distance(u, v) + | c(u) − c(v) | ≥ diameter(G) + 1.<br />
The span of a radio labelling c is the largest integer in the image of c. The radio number of a graph<br />
G is the smallest integer M such that span(c) = M for some radio labelling c. It is known that a<br />
graph of n vertices has a radio number of at least n <strong>and</strong> at most (n−1)2<br />
2<br />
+ r, where r is determined<br />
by the parity of n. This presentation discusses three-parameter graphs known as Sok graphs. We<br />
show that for all but two integers between the known minimum <strong>and</strong> maximum, there exists a Sok<br />
graph whose radio number is that integer. The results of this work entirely settle the question of<br />
what the possible radio numbers are for graphs of order n. In addition, we present a generalization<br />
of distance maximization, a well known technique for determining lower bounds of radio numbers,<br />
<strong>and</strong> show that the bounds are sharp for an infinite family of graphs.<br />
Intuition <strong>and</strong> Probability<br />
Colin Street<br />
Intuition can be a powerful <strong>to</strong>ol for day-<strong>to</strong>-day application, but it can also lead us <strong>to</strong> draw<br />
false conclusions. This talk will examine how some common cognitive biases conflict with statistics<br />
both in regular application <strong>and</strong> in some notable cases, <strong>and</strong> show how some simple applications of<br />
probability can help.<br />
Required Background : none ’
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 59<br />
Lie Group Methods for Moving Mesh Algorithms<br />
Simon Szatmari - English talk with French slides<br />
In the realm of numerical computation, the aim is <strong>to</strong> approximate with the help of a computer<br />
the solutions of a PDE with as much speed <strong>and</strong> accuracy as possible. However, some PDEs still<br />
resist our attemps <strong>to</strong> solve them numerically.<br />
Consequently, the use of Lie Groups has recently penetrated the domain of what is called<br />
Geometric Integration. More precisely, we can transform Iterative Methods in<strong>to</strong> Canonical Iterative<br />
Methods that re- spect the subjacent Lie Group structures of the PDE.<br />
My talk will focus on the following three aspects. To begin with, I will give an intuitive expla-<br />
nation of what Lie Groups are <strong>and</strong> how they work. It will be followed by a brief introduction <strong>to</strong><br />
what Moving Mesh Methods are, how they work <strong>and</strong> why they are necessary. When combining the<br />
two ideas, I will demonstrate how Lie Group Methods come about, what enhencements they bring<br />
<strong>and</strong> what new avenues of research are currently explored.<br />
Modeling Techniques of Genetic Information Flow: Past <strong>and</strong><br />
Future<br />
Caleb Tarzwell<br />
This presentation will discuss the results <strong>and</strong> findings of an NSERC-USRA funded survey con-<br />
ducted in the summer of 2012 at the University of Northern British Columbia of modeling techniques<br />
in molecular biology. Numerous mathematical models have been proposed since Francis Crick’s pro-<br />
posal of the Central Dogma of Molecular Biology. The Central Dogma has since been disproven<br />
but is still commonly used <strong>to</strong> describe the nonlinear <strong>and</strong> multidirectional flow of information be-<br />
tween the nucleus <strong>and</strong> the ribosome. An introduction <strong>to</strong> the Central Dogma <strong>and</strong> the challenging<br />
problems which arise will be provided for listeners without a background in Molecular Biology.<br />
Three promising models will be presented: finite state machines, matrix algebra with connections<br />
<strong>to</strong> group theory, <strong>and</strong> hidden markov models. These mathematical <strong>and</strong> probabilistic models attempt<br />
<strong>to</strong> describe the flow of genetic information within a cell. The most common application has been<br />
describing the transition from DNA <strong>to</strong> RNA <strong>to</strong> protein. The three models will be presented with<br />
their relative merits <strong>and</strong> weaknesses <strong>and</strong> situations in which they are best employed. After the<br />
introduction of these, a dynamic model describing the complete flow of information within the cell<br />
will be presented consisting of various components of each of the three models. Future steps for this<br />
NSERC funded survey will then be discussed. The most intriguing of these are obtaining better pre-<br />
diction mechanisms for RNA <strong>and</strong> protein structure. The presentation will conclude with discussing<br />
the need for researchers with an interdisciplinary background <strong>to</strong> bridge the differences between
60 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
methodologies between mathematicians <strong>and</strong> molecular biologists <strong>to</strong> speed further developments in<br />
molecular biology.<br />
Introducing Uniformly Distributed Sequences<br />
Arman Tavakoli<br />
I will motivate <strong>and</strong> introduce the idea of a uniformly distributed sequence using a Monte Carlo<br />
simulation. After a few example sequences, I will discuss a celebrated theorem by Hermann Weyl<br />
called Weyl’s criterion. The rest of the talk will be about different kinds of uniformly distributed<br />
sequences.<br />
Parallel Parking with Lie Algebras<br />
Selim Tawfik<br />
Using the language of Lie algebras, we will see that an idealized driver is always able <strong>to</strong> parallel<br />
park provided there is enough room for their vehicle <strong>to</strong> fit. We will start by quickly defining<br />
manifolds, vec<strong>to</strong>r fields, Lie groups, Lie algebras <strong>and</strong> Lie brackets, <strong>and</strong> stating important results<br />
connecting these notions.<br />
Required Background: Basic differential geometry would help, but not strictly necessary.<br />
Domination Polynomials of Graphs <strong>and</strong> Their Roots<br />
Julia Tufts<br />
We say that a set of vertices, S, is dominating if every vertex of the graph is in S or adjacent <strong>to</strong><br />
a vertex in S. The domination polynomial of a graph G is the generating function of the number<br />
of dominating sets of each size in G.<br />
The domination polynomial is a relatively new polynomial, <strong>and</strong> as is the case with other graph<br />
polynomials, the roots are of great interest. This talk will discuss the nature <strong>and</strong> location of the<br />
roots of domination polynomials. We find that the roots for certain families of graphs often create<br />
distinct patterns that we are able <strong>to</strong> analyze, <strong>and</strong> we also obtain a surprising result for the set of<br />
all domination roots.
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 61<br />
Opportunities in Mathematical Biology<br />
Rebecca Tyson<br />
Mathematical Biology is an exciting discipline at the interface of mathematics <strong>and</strong> biology. Many<br />
biological questions are intractable when approached with biological techniques alone, but can be<br />
solved with the power of mathematical <strong>to</strong>ols. The breadth <strong>and</strong> variety of the field is enormous,<br />
from differential equation modelling of forest fires or the inner workings of cells <strong>to</strong> interacting<br />
particle systems models of recolonization or evolutionary processes. We begin the session with an<br />
introduction <strong>to</strong> the field given by three speakers from the University of British Columbia, <strong>Okanagan</strong><br />
<strong>and</strong> Vancouver <strong>campus</strong>es, <strong>and</strong> the University of Alberta. We then discuss graduate programs in<br />
mathematical biology in Canada, <strong>and</strong> future careers.<br />
Knapsack-Based Cry<strong>to</strong>graphy<br />
Michael Wanless<br />
At the heart of every public-key cryp<strong>to</strong>system is a computationally difficult problem that pro-<br />
vides security for the system. Thus, problems that are known <strong>to</strong> be hard hold a lot of interest for<br />
cryp<strong>to</strong>logists <strong>and</strong> number theorists in general. An example of such a problem is the knapsack or<br />
subset-sum problem, which is proven <strong>to</strong> be NP-complete. This talk will provide an introduction <strong>to</strong><br />
the ideas behind classical public-key cryp<strong>to</strong>systems based upon the knapsack problem, using the<br />
Merkle-Hellman cryp<strong>to</strong>system as a case-study. We will examine how the security of these cryp-<br />
<strong>to</strong>systems is tied <strong>to</strong> finding short vec<strong>to</strong>rs in lattices, <strong>and</strong> thus how the LLL algorithm can be used<br />
<strong>to</strong> break many such systems.<br />
Prerequisites: An underst<strong>and</strong>ing of modular arithmetic is nearly esse<br />
The Shortest Introduction <strong>to</strong> Semidefinite Programming<br />
Gwen Yun Weng<br />
Semidefinite programs often capture the mathematical essence of problems of various structures.<br />
Therefore, semidefinite programming is used in theoretical <strong>and</strong> practical explorations of a wide range<br />
of problems. This talk will cover the very basics of semidefinite programming <strong>and</strong> demonstrate its<br />
application <strong>to</strong> a typical eigenvalue optimization problem.<br />
Required background: Basic Linear Algebra. Exposure <strong>to</strong> Linear Programming will be helpful.
62 CHAPTER 3. ABSTRACTS / RÉSUMÉS<br />
Game Theory <strong>and</strong> Evolution<br />
Toban Wiebe<br />
Game theory is essential for underst<strong>and</strong>ing evolution. Organisms are in competition for survival;<br />
as such, there is a strategic aspect <strong>to</strong> natural selection. This talk will provide an introduction <strong>to</strong><br />
game theory <strong>and</strong> its use in modelling evolution. Classical game theory examines equilibria produced<br />
by rational players using optimal strategies. Evolutionary game theory adds an extra stability<br />
condition for equilibrium: that no small mutant population can invade a population in equilibrium.<br />
The model can be further extended <strong>to</strong> analyze the dynamics of evolution. No prior knowledge of<br />
game theory is required.<br />
A Winning Strategy<br />
Wu, Steven<br />
Billions are poured in<strong>to</strong> a gambling industry annually that is designed for the house edge <strong>to</strong><br />
rake in profits. A New York Times bestseller written by Edward O. Thorp resulted from the<br />
phenomenon discovered that flipped the odds of one casino game, Blackjack, in favour <strong>to</strong> the<br />
player. After a brief overview on the rules of how <strong>to</strong> play, features that distinguish it as capable of<br />
a positive expectation for the player, I will detail the pertinent mathematics that explain how each<br />
unique rule, from doubling down <strong>to</strong> the option of taking insurance, affects the expectation of the<br />
game. After describing what constitutes “Basic Strategy”, I will show how Thorp manipulated the<br />
probabilities using card counting <strong>to</strong> produce a winning strategy that swept the nation through use<br />
of examples of certain game scenarios.<br />
Required background: None, previous knowledge of the rules of Blackjack <strong>and</strong> expected value will<br />
help <strong>to</strong> follow along.<br />
Statistical Refinement of Astrophysical Numerical Simulations<br />
Miayan Yeremi<br />
The process of star formation is the fundamental agent at determining how an isolated galaxy<br />
like our own evolves over the course of the universe. Many physical processes contribute <strong>to</strong> star<br />
formation (gravitation, magnetism, chemistry, radiation, <strong>and</strong> fluid dynamics). However, it is not<br />
unders<strong>to</strong>od exactly how these effects shape the process of star formation. Physical observations
3.2. STUDENT ABSTRACTS / RÉSUMÉS DES ÉTUDIANTS 63<br />
from radio telescopes provide some insight in<strong>to</strong> the process of star formation but alone do not<br />
provide the necessary information <strong>to</strong> underst<strong>and</strong> exactly how the physical process evolves. Properly<br />
designing <strong>and</strong> experiment <strong>to</strong> study star formation is complicated by many fac<strong>to</strong>rs. A single run<br />
of the computer model can take upwards of five thous<strong>and</strong> hours, in addition some of the input<br />
variables evolve during the code runs meaning that the inputs of the computer code are observed<br />
with error. Lastly, comparing code runs <strong>to</strong> physical observations is complicated by things, first we<br />
must compare three dimensional data cubes <strong>and</strong> secondly simple euclidean distances between these<br />
cubes is not correct measure of similarity between these two objects. In this talk we will discuss<br />
some recent work on the design <strong>and</strong> analysis of complex experiments <strong>to</strong> study star formation. The<br />
ultimate gal of this study is <strong>to</strong> provide a physically meaningful description of how stars evolve.<br />
How Topologically Inclined Thieves Split Their Spoils<br />
Jonathan Zung<br />
More often than one might expect, a pair of thieves is confronted with the following problem.<br />
Having s<strong>to</strong>len a necklace with k different types of jewels, they wish <strong>to</strong> cut up the necklace so that<br />
each of the two receives the same number of jewels of each type. In 1985, thieves the world over<br />
rejoiced when Douglas West <strong>and</strong> Charles Goldberg showed us how <strong>to</strong> split such necklaces equitably<br />
with at most k cuts. Amazingly, their approach uses a <strong>to</strong>pological argument. In this talk, I will<br />
present a slick proof of this result due <strong>to</strong> Alon <strong>and</strong> West.
General Information /<br />
Informations générales<br />
4.1 Internet connections on <strong>campus</strong> / Connexions Internet<br />
sur les <strong>campus</strong><br />
UBC’s <strong>Okanagan</strong> <strong>campus</strong><br />
Connect <strong>to</strong> the network “ubcvisi<strong>to</strong>r”. You will be directed <strong>to</strong> a website where you must enter in<br />
your email <strong>to</strong> log on.<br />
Se connecter au réseau “ubcvisi<strong>to</strong>r”. Vous serez dirigés vers une page qui vous dem<strong>and</strong>e un email<br />
pour s’inscrire.<br />
<strong>Okanagan</strong> College<br />
<strong>Okanagan</strong> College does not have a visi<strong>to</strong>r network that we can use. The school has provided us<br />
with a few usernames <strong>and</strong> passwords if you require internet for your presentation. These can be<br />
used for presentations only. The volunteer in your presentation room can issue you a username <strong>and</strong><br />
password <strong>to</strong> use if you need it.<br />
L’<strong>Okanagan</strong> College n’a pas de réseau pour les visiteurs. L’école nous a donné quelques noms et<br />
mots de passe pour ceux qui auront besoin d’une connexion internet pour leur présentation. Ils ne<br />
sont disponibles que pour les présentations. Le bénévole de votre salle de présentation s’occupera<br />
de vous les fournir.<br />
64
4.2. GETTING TO/FROM OKANAGAN COLLEGE AND THE CLOSING BANQUET 65<br />
4.2 Getting <strong>to</strong>/from <strong>Okanagan</strong> College <strong>and</strong> the closing ban-<br />
quet<br />
There will be a day of talks held at <strong>Okanagan</strong> College (OC), 1000 KLO Rd, on Friday, July 13th.<br />
All talks will be held in Building E, The Centre for Learning.<br />
The closing banquet, will be held at the Ramada Hotel, 2170 Harvey Ave (Hwy 97N).<br />
Buses have been arranged <strong>to</strong> transport people <strong>to</strong>/from UBC’s <strong>Okanagan</strong> <strong>campus</strong> <strong>to</strong> OC <strong>and</strong><br />
<strong>to</strong>/from the Ramada Hotel for the closing banquet. If you need a ride <strong>to</strong> OC or the closing<br />
banquet, please sign up for the buses so that we can ensure everyone at the conference who needs<br />
a ride gets one. If you do not sign up for a bus, or you miss your bus, we cannot guarantee that<br />
you will be able <strong>to</strong> get on the next one.<br />
Public transport does go <strong>to</strong> each of the venues. To get <strong>to</strong> OC from UBC take the #8 - <strong>Okanagan</strong><br />
College <strong>and</strong> get off at <strong>Okanagan</strong> College. To get <strong>to</strong> the Ramada Hotel from UBC take the #97 -<br />
Express, get off at Cooper Rd near Orchard Park Mall, <strong>and</strong> walk approximately 450m east <strong>to</strong> the<br />
Ramada.<br />
If you are driving <strong>to</strong> any of the venues, there is parking available. OC Facilities has <strong>to</strong>ld us that<br />
parking is free of charge on the day we are there. Parking is not free at UBC’s <strong>Okanagan</strong> <strong>campus</strong>;<br />
you must purchase a parking pass from one of the ticket dispensers. If you decide <strong>to</strong> drive <strong>to</strong> the<br />
closing banquet, please decide on a designated driver beforeh<strong>and</strong>. Please do not drink <strong>and</strong> drive!<br />
You are also more than welcome <strong>to</strong> leave your vehicle overnight at the Ramada <strong>and</strong> take the bus<br />
back <strong>to</strong> the university, or one of the volunteers can arrange a cab for you.<br />
Aller et revenir de <strong>Okanagan</strong> college et du banquet final<br />
Une journée de présentation sera tenue au <strong>Okanagan</strong> College (OC), 1000 KLO Rd, le vendredi<br />
13 juillet. Toutes les présentations seront donnes au Pavillon E, The Centre for Learning.<br />
Le banquet final se tiendra au Ramada Hotel, 2170 Harvey Ave (Hwy 97N).<br />
Un transport en au<strong>to</strong>bus a été prévu pour l’aller et le re<strong>to</strong>ur entre le <strong>campus</strong> de UBC <strong>Okanagan</strong><br />
et l’<strong>Okanagan</strong> College ainsi que pour le banquet final au Ramada Hotel. S vous avez besoin d’un<br />
transport vers l’<strong>Okanagan</strong> College pour le banquet final, veuillez vous inscrire afin de s’assurer que<br />
<strong>to</strong>us ceux qui auront besoin d’un transport en auront un. Si vous ne vous inscrivez pas ou que vous<br />
manquez votre au<strong>to</strong>bus, nous ne pouvons pas vous assurer que vous pourrez prendre le prochain<br />
transport.<br />
Le réseau d’au<strong>to</strong>bus dessert l’<strong>Okanagan</strong> College. Pour se rendre à ’C de UBC, prenez l’au<strong>to</strong>bus<br />
#8 - <strong>Okanagan</strong> College et sortez à l’arrêt <strong>Okanagan</strong> College. Pour aller au Ramada Hotel à partir<br />
de UBC, prenez l’au<strong>to</strong>bus #97 - Express, sotez à Cooper Rd près de Orchard Park Mall et marchez
66 CHAPTER 4. GENERAL INFORMATION / INFORMATIONS GÉNÉRALES<br />
environ 450m vers l’est.<br />
Si vous vous rendez en au<strong>to</strong>mobile à l’un de ces deux endroits, des stationnements seront<br />
disponibles. Les stationnements de l’OC seront gratuits lors de notre passage. Le stationnement<br />
n’est pas gratuit sur le <strong>campus</strong> de UBC; vous devez acheter un ticket de stationnement à l’une des<br />
bornes. Si vous décider de conduire pour vous rendre au banquet, décidez d’un conducteur désigné.<br />
S’il vous plait, ne conduisez pas après avoir bu! Vous pouvez aussi laisser votre véhicule sur les<br />
lieux du banquet final et prendre l’au<strong>to</strong>bus. Il est aussi possible d’appeler un taxi.<br />
Friday, July 13 - Vendredi 13 juillet<br />
• Sign-up for buses <strong>to</strong> <strong>Okanagan</strong> College will happen Thursday, July 12th during coffee breaks<br />
<strong>and</strong> lunch. People presenting on Friday need <strong>to</strong> be on the 7:45am bus <strong>to</strong> pre-load presentations.<br />
• Sign-up for buses <strong>to</strong> UBC <strong>Okanagan</strong> will happen Friday, July 13th during coffee breaks <strong>and</strong><br />
lunch.<br />
• L’inscription pour les au<strong>to</strong>bus vers <strong>Okanagan</strong> College aura lieu le jeudi 12 juillet durant<br />
les pauses-caf et l’heure du midi. Les participants qui donnent une présentation le vendredi<br />
doivent prendre l’au<strong>to</strong>bus de 7h45 afin de transférer leur diaporama.<br />
• L’inscription pour les au<strong>to</strong>bus vers UBC <strong>Okanagan</strong> aura lieu le vendredi 13 juillet durant les<br />
pauses-ca’e et l’heure du midi.<br />
Leave/Départ Arriving / Arrivée Bus/ Au<strong>to</strong>bus<br />
7:45 8:05 <strong>to</strong>/vers <strong>Okanagan</strong> College (2 buses)<br />
8:25 8:45 <strong>to</strong>/vers <strong>Okanagan</strong> College (2 buses)<br />
18:30 18:50 <strong>to</strong>/vers UBC <strong>Okanagan</strong>, via Sc<strong>and</strong>ia<br />
19:20 19:30 <strong>to</strong>/vers UBC <strong>Okanagan</strong>, via Sc<strong>and</strong>ia<br />
19:50 20:10 <strong>to</strong>/vers UBC <strong>Okanagan</strong><br />
20:30 20:50 <strong>to</strong>/vers UBC <strong>Okanagan</strong> (WIMS participants only)
4.3. KELOWNA TRANSIT INFORMATION / LE TRANSPORT EN COMMUN Á KELOWNA67<br />
Saturday, July 14th - Samedi 14 juillet<br />
• Sign-up for buses <strong>to</strong> the Ramada Hotel will happen Saturday, July 14th during coffee breaks<br />
<strong>and</strong> lunch.<br />
• There is no sign-up required for buses leaving the Ramada Hotel.<br />
• L’inscription pour les au<strong>to</strong>bus vers le Ramada Hotel aura lieu le samedi 14 juillet durant les<br />
pauses-ca’e et l’heure du midi.<br />
• Il n’y a pas d’inscription préalable pour les au<strong>to</strong>bus du Ramada Hotel vers UBC <strong>Okanagan</strong>.<br />
Leave/Départ Arriving / Arrivée Bus/ Au<strong>to</strong>bus<br />
17:30 17:40 <strong>to</strong>/vers <strong>Okanagan</strong> College (2 buses)<br />
18:00 18:10 <strong>to</strong>/vers <strong>Okanagan</strong> College (2 buses)<br />
22:30 22:40 <strong>to</strong>/vers UBC <strong>Okanagan</strong>, via Sc<strong>and</strong>ia<br />
23:30 23:40 <strong>to</strong>/vers UBC <strong>Okanagan</strong>, via Sc<strong>and</strong>ia<br />
0:30 0:40 <strong>to</strong>/vers UBC <strong>Okanagan</strong><br />
1:00 1:10 <strong>to</strong>/vers UBC <strong>Okanagan</strong> (WIMS participants only)<br />
4.3 <strong>Kelowna</strong> transit information / Le transport en commun<br />
á <strong>Kelowna</strong><br />
The main bus that travels between UBC <strong>Okanagan</strong> <strong>campus</strong> <strong>and</strong> down<strong>to</strong>wn is the 97 - Express. The<br />
bus that runs from UBC <strong>to</strong> <strong>Okanagan</strong> College <strong>to</strong> down<strong>to</strong>wn is the 8 - <strong>Okanagan</strong> College. Fare for<br />
public transport is $2.25 <strong>and</strong> drivers carry no change.<br />
You can view <strong>Kelowna</strong> transit schedules <strong>and</strong> maps at www.transitbc.com/regions/kel.<br />
L’au<strong>to</strong>bus principal qui dessert le <strong>campus</strong> de l’Université ainsi que le centre-ville est le #97-<br />
Express. L’au<strong>to</strong>bus qui fait le parcours du <strong>Okanagan</strong> College vers le centre-ville est le #8-<strong>Okanagan</strong><br />
College. Le coût d’un aller est de 2,75$. Ayez l’argent exact puisque les conducteurs n’ont pas de<br />
monnaie.<br />
Vous pouvez trouver <strong>to</strong>us les trajets d’au<strong>to</strong>bus et les horaire au www.transitbc.com/regions/kel.
68 CHAPTER 4. GENERAL INFORMATION / INFORMATIONS GÉNÉRALES
4.4. GREAT PLACES TO EAT IN KELOWNA / BONS ENDROITS OÙ MANGER À KELOWNA69<br />
4.4 Great places <strong>to</strong> eat in <strong>Kelowna</strong> / Bons endroits où manger<br />
à <strong>Kelowna</strong><br />
Breakfast / Déjeuners<br />
The Jammery, 8038 Hwy 97 N, www.jammery.com ($)<br />
Bread Co., 363 Bernard Ave, thebreadcompany.ca ($)<br />
Bohemian Cafe, 524 Bernard Ave, www.bohemiancater.com ($$)<br />
Cafes / Cafés<br />
The Cannery, 1289 Ellis St ($)<br />
The Bean Scene, 274 Bernard Ave ($)<br />
Lunch / Dîners<br />
Bread Co., 363 Bernard Ave, thebreadcompany.ca ($)<br />
Mediterranean Market, 1570 Gordon Dr ($)<br />
Wood Fire Bakery, 2041 Harvey Ave ($$)<br />
Dinner / Soupers<br />
Pubs<br />
Fern<strong>and</strong>o’s Taqueria, 279 Bernard Ave ($$)<br />
Twisted Toma<strong>to</strong>, 371 Bernard Ave, twisted<strong>to</strong>ma<strong>to</strong>kitchen.com ($$)<br />
Poppadoms - Taste India!, 948 McCurdy Rd, www.poppadoms.ca ($$)<br />
DunnEnzie’s Pizza, 1559 Ellis St, www.dunnenzies.com ($$)<br />
Mon Thong Thai, 1876 Cooper Rd, www.monthong.ca ($$)<br />
RauDZ, 1560 Water St, www.raudz.com ($$$)<br />
Doc Willoughby’s Pub, 353 Bernard Avenue, www.docwilloughby.com ($$)<br />
O’ Flannigan’s Pub , 319 Queensway ($$)<br />
Rose’s Waterfront Pub, 1352 Water St, www.rosespub.com ($$)<br />
Turtle Bay Pub, 2850 Woodsdale Rd, Lake Country, www.turtlebaypub.com ($$)<br />
$ under 10 per entree / Moins de 10 $<br />
$$ 10-15 per entree / Entre 10 $ et 15 $<br />
$$$ 15-25 per entree / Entre 15$ et 25$
70 CHAPTER 4. GENERAL INFORMATION / INFORMATIONS GÉNÉRALES<br />
4.5 Fun things <strong>to</strong> do in <strong>Kelowna</strong> / Activités amusantes à<br />
<strong>Kelowna</strong>:<br />
Knox Mountain<br />
Located north of the down<strong>to</strong>wn area, about a 25min walk or 5min drive north from Queensway<br />
Bus Loop, down Ellis St. Alternatively, you can bus there on the #2 - North End Shuttle<br />
<strong>and</strong> get off at Cambridge Ave˙<strong>and</strong> Ellis St. There are many walking trails on this mountain,<br />
short, long, steep, <strong>and</strong> gentle. You may find people mountain biking on the trails. There<br />
is a look out halfway up <strong>and</strong> another at the <strong>to</strong>p, which you can also drive <strong>to</strong> if you have a<br />
vehicle. From here you can take in the beautiful views of <strong>Okanagan</strong> Lake <strong>and</strong> its surrounding<br />
mountains, stretching off in<strong>to</strong> the horizon. Take good walking shoes <strong>and</strong> plenty of water!<br />
Cette montagne est située au nord de la région du centre-ville, à environ 25 minutes de marche<br />
ou 5 minutes de voiture au nord de Queensway Bus Loop, sur Ellis St. Vous pouvez aussi<br />
vous y rendre en au<strong>to</strong>bus en prenant la #2 - North End Shuttle et en descendant au coin<br />
Cambridge Ave. et Ellis St. On retrouve sur cette montagne plusieurs pistes de r<strong>and</strong>onnée,<br />
qu’elles soient courtes ou longues, abruptes ou douces. Certains font même de la bicyclette<br />
sur ces pistes. Il y a un point de vue à mi-chemin et un autre, au sommet de la montagne,<br />
où vous pouvez vous rendre en voiture. De là, vous pourrez admirer l’<strong>Okanagan</strong> Lake et les<br />
montagnes avoisinantes qui s’étendent jusqu’á l’horizon. N’oubliez pas de bons souliers de<br />
marche et beaucoup d’eau!<br />
City Park <strong>and</strong> Beach<br />
Located a hop, step, <strong>and</strong> a skip away from down<strong>to</strong>wn <strong>Kelowna</strong>, at the end of Bernard Ave<br />
<strong>and</strong> parallel <strong>to</strong> Abbott St, City Park <strong>and</strong> its beach, on <strong>Okanagan</strong> Lake, is a great place <strong>to</strong><br />
people watch, go swimming, <strong>and</strong> relax in the sun. Take your swimsuit <strong>and</strong> <strong>to</strong>wel!<br />
Situés <strong>to</strong>ut près du centre-ville de <strong>Kelowna</strong>, au bout de Bernard Ave. et paralèle Abbott<br />
St., City Park et sa plage sur le bord de l’<strong>Okanagan</strong> Lake sont un bel endroit où aller pour<br />
admirer la vue, se baigner et relaxer un peu au soleil. Apportez avec vous votre maillot de<br />
bain et votre serviette!<br />
Beyond the Crux<br />
This climbing gym is located at #2 - 1414 Hunter Court. There are walls are fixed with au<strong>to</strong><br />
belays so that you can climb away <strong>to</strong> your heart’s content! A day pass is $15 <strong>and</strong> it is open
4.5. FUN THINGS TO DO IN KELOWNA / ACTIVITÉS AMUSANTES À KELOWNA: 71<br />
Monday <strong>to</strong> Friday, 4 - 10pm <strong>and</strong> Saturday, 11am - 5pm. For more information check out<br />
www.beyondthecrux.info.<br />
Ce gymnase d’escalade est situ au # 2 - 1414 Hunter Court. Il y a des murs équipés d’au<strong>to</strong>-<br />
assureurs pour que vous puissiez grimpez autant que vous le voulez. La passe de journée coûte<br />
15$ et le centre est ouvert du lundi au vendredi de 16h à 22h ainsi que le samedi de 11h à<br />
17h. Pour plus d’information: www.beyondthecrux.info.<br />
Rusty’s Steakhouse<br />
Don’t let the name fool you, this is a billiard hall. They have 10-12 tables for just food <strong>and</strong><br />
have a full menu available that can be brought <strong>to</strong> the tables. The key bonus for this place<br />
is they have a lot of tables, <strong>and</strong> it’s very far from a ’dirty pool hall’ - very open space, not<br />
smoky, newly renovated, clientele are mostly students <strong>and</strong> middle aged men... Located at #1<br />
- 1525 Dilworth Dr. Checkout www.rustyssteakhouse.ca for more information.<br />
Ne laissez pas le nom vous tromper, il s’agit d’une salle de billard. Une dizaine de tables sont<br />
disponibles pour manger et un menu complet est fait pour être servi directement aux tables de<br />
billard. L’avantage de l’endroit est qu’il y a un gr<strong>and</strong> nombre de tables et qu’il n’y a aucune<br />
comparaison à faire avec les bars de billard miteux -tràs ouvert, pas enfumé, nouvellement<br />
rénové, la clientèle est constituée en gr<strong>and</strong>e partie d’étudiants et de jeunes hommes. Situé au<br />
#1 - 1525 Dilworth Dr. Allez au www.rustyssteakhouse.ca pour plus d’informations.<br />
Walk the Mission Creek Greenway<br />
The Greenway is a 17km pathway that runs throughout <strong>Kelowna</strong> from Lakeshore Drive, near<br />
the lake at Truswell Rd, up <strong>to</strong> the Rutl<strong>and</strong> <strong>and</strong> Black Mountain areas. It is a gentle walk <strong>and</strong><br />
is used by many Kelownians for walking, running, biking, <strong>and</strong> horseback riding along Mission<br />
Creek. For more information check out www.greenway.kelowna.bc.ca.<br />
Le voie verte est une voie de 17 kilomètres de sentiers traversent <strong>Kelowna</strong> à partir de Lakeshore<br />
Drive, près du lac à la route Truswell Rd, jusqu’à Rutl<strong>and</strong> et au secteur Black Mountain. C’est<br />
un trajet accessible utilisé par les habitants de <strong>Kelowna</strong> pour marcher, courir, faire du vélo<br />
et du cheval. Pour plus d’informations, visitez le www.greenway.kelowna.bc.ca.<br />
Walk along the waterfront<br />
A great place <strong>to</strong> go for a stroll is the path along the waterfront. It runs parallel <strong>to</strong> Water St,<br />
starting down<strong>to</strong>wn at the corner of Bernard Ave <strong>and</strong> Abbott St, travelling north <strong>to</strong> Waterfront
72 CHAPTER 4. GENERAL INFORMATION / INFORMATIONS GÉNÉRALES<br />
Park. Here you’ll find a quiet beach <strong>to</strong> chill out on. If you continue <strong>to</strong> the very end you’ll<br />
come <strong>to</strong> a peaceful waterfowl sanctuary with a boardwalk running through it.<br />
L’endroit parfait pour prendre une marche est la rive du lac <strong>Okanagan</strong>. Les quais sont<br />
paralléles á Water St, partant au centre-ville au coin de Bernard Ave et Abbott St, jusqu’au<br />
nord á Waterfront Park. Á cet endroit, vous trouverez une jolie plage pour relaxer. Au bout<br />
de cette plage se trouve un endroit magnifique qui vaut le dé<strong>to</strong>ur.<br />
4.6 <strong>CUMC</strong> 2013 Host Bids / Enchères pour accueillir le CCÉM<br />
2013<br />
The <strong>CUMC</strong> could not continue without its host school. We strongly encourage you <strong>to</strong> consider<br />
making a bid <strong>to</strong> host <strong>CUMC</strong> 2013 at your school. First you need <strong>to</strong> check with your home depart-<br />
ment <strong>to</strong> get approval for hosting. Once you get approval, inform one of the organizers that your<br />
school would like <strong>to</strong> put in a bid for <strong>CUMC</strong> 2013.<br />
On Friday, July 13th at 5:30pm, representatives from each university that wish <strong>to</strong> be considered<br />
as next year host university will give a brief presentation about their school <strong>and</strong> city. Ballots will<br />
be distributed following the presentations <strong>and</strong> will be collected at lunch on Saturday, July 14. Each<br />
participating university is given one vote, regardless of how many of its students are attending the<br />
conference. In a change from previous years, the winner will be decided using the Schulze Method,<br />
a modern <strong>and</strong> widely-used voting system that uses a preferential ballot. Rather than voting for<br />
a single option, each university’s ballot will allow the c<strong>and</strong>idate host universities <strong>to</strong> be ranked in<br />
order of preference. The preferential ballots will then be input in<strong>to</strong> a computer which uses the<br />
Schulze Method <strong>to</strong> determine the winner. We have chosen <strong>to</strong> use the Schulze Method because it<br />
is mathematically interesting, it is modern, it satisfies an extremely wide range of academic voting<br />
system criteria (Condorcet criterion, majority criterion, independence of clones, etc.), <strong>and</strong> it has<br />
been adopted by many reputable organizations such as the Wikimedia Foundation. The winning<br />
host university will be announced at the closing banquet.<br />
Enchères pour accueillir le CCÉM 2013<br />
Le CCÉM ne peut pas exister sans une université hôte pour l’accueillir. Nous vous invi<strong>to</strong>ns à<br />
penser à la possibilité de participer à l’enchère pour organiser l’évènement ln prochain. La première<br />
chose à faire serait de véfifier si le département de mathématiques de votre université est favorable<br />
à une telle c<strong>and</strong>idature. Une fois lu<strong>to</strong>risation obtenue, informez un organisateur que votre école<br />
aimerait déposer sa c<strong>and</strong>idature.
4.6. <strong>CUMC</strong> 2013 HOST BIDS / ENCHÈRES POUR ACCUEILLIR LE CCÉM 2013 73<br />
Le vendredi 13 juillet à 17:30, les représentants de chaque université participant à lnchère don-<br />
neront une brève présentation à propos de leur école et de leur ville. Les bulletins de vote seront<br />
distribués suite aux présentations et seront rammassés le midi suivant. Chaque université partici-<br />
pante a droit à un vote, peu importe le nombre d’étudiants présents. Contrairement aux dernières<br />
années, le gagnant sera déterminé par la méthode de Schulze, une méthode de vote moderne et<br />
largement utilisée qui utilise un vote à classement. Au lieu de voter pour une seule université,<br />
chaque bulletin permettra de voter pour une liste d’universités disposées en ordre de préférence.<br />
Le gagnant sera ensuite nommé par un ordinateur. Cette méthode a été choisie car elle est intéres-<br />
sante dn point de vue mathématique, elle est moderne, elle satisfait une gr<strong>and</strong>e partie des critères<br />
d’un vote (critère de Condorcet, critère de majorité, indépendance des clônes, etc.), et elle a été<br />
adoptée par des organisations reconnues comme la fondation Wikimedia. L’université gagnante sera<br />
annoncée au banquet de clôture du congrès.
74 CHAPTER 4. GENERAL INFORMATION / INFORMATIONS GÉNÉRALES<br />
4.7 Sponsors / Comm<strong>and</strong>itaires<br />
Official Sponsor / Partenaire Officiel<br />
Welcome <strong>to</strong> <strong>Kelowna</strong>, <strong>and</strong> <strong>to</strong><br />
UBC’s <strong>Okanagan</strong> <strong>campus</strong>.<br />
PROFESSOR WESLEY PUE<br />
Provost <strong>and</strong> Vice Principal<br />
UBC’s <strong>Okanagan</strong> <strong>campus</strong><br />
The University of British Columbia is very proud <strong>to</strong> host so many outst<strong>and</strong>ing<br />
undergraduate researchers at the 2012 <strong>Canadian</strong> Undergraduate Mathematics<br />
Conference. We encourage you <strong>to</strong> get <strong>to</strong> know our <strong>Okanagan</strong> <strong>campus</strong> <strong>and</strong> the many<br />
advantages of pursuing your studies here at UBC.<br />
Our <strong>Okanagan</strong> <strong>campus</strong> offers a diverse range of thesis-based interdisciplinary graduate<br />
studies — from the humanities <strong>and</strong> creative arts <strong>to</strong> social <strong>and</strong> natural sciences.<br />
Learn. Share. Enjoy. We look forward <strong>to</strong> welcoming you again as you prepare for an<br />
exciting future in whichever fields of endeavour your passion for mathematics takes you.
4.7. SPONSORS / COMMANDITAIRES 75<br />
<strong>Okanagan</strong> College is pleased <strong>to</strong> welcome the<br />
participants of the <strong>Canadian</strong> Undergraduate<br />
Mathematics Conference. With four <strong>campus</strong>es spread<br />
throughout the <strong>Okanagan</strong> Valley, the College offers a broad range<br />
of career, continuing education, degree, developmental, trades <strong>and</strong><br />
technologies, university studies, <strong>and</strong> vocational programs – including<br />
a Mathematics <strong>and</strong> Statistics Department that offers a wide variety of<br />
first- <strong>and</strong> second-year courses in mathematics <strong>and</strong> statistics that are<br />
eligible for transfer <strong>to</strong> post-secondary institutions across Canada.<br />
The College’s participation in this conference has been sponsored<br />
<strong>and</strong> supported by the Science, Technology <strong>and</strong> Health <strong>and</strong> Social<br />
Development portfolio, the <strong>Okanagan</strong> College Faculty Association<br />
(OCFA), the Applied Science Technologists <strong>and</strong> Technicians of British<br />
Columbia (ASTTBC) <strong>and</strong> the British Columbia Women in Technology<br />
(BCWIT).<br />
The Science, Technology <strong>and</strong> Health <strong>and</strong> Social Development portfolio<br />
includes 17 different programs that serve more than 1,000 students at<br />
all four of <strong>Okanagan</strong> College’s regional <strong>campus</strong>es. The portfolio acts<br />
as a stepping s<strong>to</strong>ne for a wide variety of careers <strong>and</strong> for further postsecondary<br />
education.<br />
The OCFA represents more than 200 faculty members of <strong>Okanagan</strong><br />
College. It serves <strong>to</strong> maintain <strong>and</strong> promote the professional status of<br />
the members of the Association, <strong>to</strong> regulate relations between faculty<br />
<strong>and</strong> <strong>Okanagan</strong> College through collective bargaining, <strong>and</strong> <strong>to</strong> function<br />
as a trade union pursuant <strong>to</strong> the laws of British Columbia.<br />
ASTTBC is the professional association that governs applied science<br />
technologists, certified technicians <strong>and</strong> a number of technical<br />
specialists <strong>and</strong> is charged with regulating the st<strong>and</strong>ards of training<br />
<strong>and</strong> practice of <strong>and</strong> for its members <strong>and</strong> protecting the interests of the<br />
public. With more than 10,000 registrants, ASTTBC is one of the larger<br />
professional associations in B.C. <strong>and</strong> maintains high academic, <strong>and</strong><br />
professional practice st<strong>and</strong>ards.<br />
The BCWIT focuses on raising the profile of women working in<br />
technology <strong>to</strong> capture the interest of girls at a younger age through<br />
h<strong>and</strong>s on events, <strong>and</strong> focused career counselling. The organization was<br />
established following a survey by ASTTBC which revealed only nine<br />
percent of its members are women.<br />
<strong>Okanagan</strong> College<br />
Science, Technology,<br />
<strong>and</strong> Health <strong>and</strong><br />
Social Development
76 CHAPTER 4. GENERAL INFORMATION / INFORMATIONS GÉNÉRALES<br />
THE IRVING K. BARBER<br />
SCHOOL OF ARTS AND SCIENCES<br />
Be here<br />
Be inspired<br />
Study hard<br />
Focus<br />
Optimize<br />
Connect<br />
Have fun<br />
Imagine<br />
Philosophize<br />
Compute<br />
Connect<br />
Set goals<br />
Achieve goals<br />
Calculate<br />
Explore<br />
Research<br />
Collaborate<br />
Be remarkable<br />
54 undergraduate<br />
programs<br />
7graduate<br />
programs<br />
1<br />
exceptional<br />
learning<br />
experience<br />
GET INSPIRED<br />
www.ubc.ca/okanagan/ikbarberschool
4.7. SPONSORS / COMMANDITAIRES 77<br />
Silver Sponsor / Partenaire Argent<br />
Pacific Institute for the Mathematical Sciences<br />
Bronze Sponsor / Partenaire Bronze<br />
<strong>Canadian</strong> Mathematical<br />
Society<br />
Westcoast Women in<br />
Engineering, Science<br />
& Technology<br />
Applied Science<br />
Technologists &<br />
Technicians of BC<br />
Centre de Recherche<br />
Mathématiques<br />
CMS Women in Math<br />
Committee
78 CHAPTER 4. GENERAL INFORMATION / INFORMATIONS GÉNÉRALES<br />
Contribu<strong>to</strong>rs / Contributeurs<br />
Golden Key<br />
International Honour<br />
Society<br />
Department of<br />
Mathematics <strong>and</strong><br />
Statistics, UNBC<br />
The <strong>Canadian</strong> Society for<br />
His<strong>to</strong>ry <strong>and</strong> Philosophy<br />
of Mathematics<br />
4.8 Riddles <strong>and</strong> Games / Énigmes et Jeux<br />
Crates of Fruit<br />
UBC’s <strong>Okanagan</strong><br />
Campus AVP Students<br />
You are on an isl<strong>and</strong> <strong>and</strong> there are three crates of fruit that have washed up in front of you. One<br />
crate contains only apples. One crate contains only oranges. The other crate contains both apples<br />
<strong>and</strong> oranges.<br />
Each crate is labeled. One reads “apples”, one reads “oranges”, <strong>and</strong> one reads “apples <strong>and</strong><br />
oranges”. You know that NONE of the crates have been labeled correctly - they are all wrong.<br />
If you can only take out <strong>and</strong> look at just one of the pieces of fruit from just one of the crates,<br />
how can you label ALL of the crates correctly?<br />
Explain Eleva<strong>to</strong>r<br />
A Man works on the 10th floor <strong>and</strong> always takes the eleva<strong>to</strong>r down <strong>to</strong> ground level at the end of<br />
the day. Yet every morning he only takes the eleva<strong>to</strong>r <strong>to</strong> the 7th floor <strong>and</strong> walks up the stairs <strong>to</strong><br />
the 10th floor, even when is in a hurry. Why?<br />
Five Gears<br />
There are five gears connected in a row, the first one is connected <strong>to</strong> the second one, the second<br />
one is connected <strong>to</strong> the third one, <strong>and</strong> so on.<br />
How much faster would the last gear be if the second gear was twice the size of the first gear,<br />
<strong>and</strong> all the other gears were the same size as the first gear?
4.8. RIDDLES AND GAMES / ÉNIGMES ET JEUX 79<br />
Rope Burning Puzzle<br />
There are two lengths of rope. Each one can burn in exactly one hour. They are not necessarily<br />
of the same length or width as each other. They also are not of uniform width (may be wider in<br />
middle than on the end), thus burning half of the rope is not necessarily 1/2 hour.<br />
By burning the ropes, how do you measure exactly 45 minutes worth of time?
80 CHAPTER 4. GENERAL INFORMATION / INFORMATIONS GÉNÉRALES<br />
33333 puzzle<br />
Use each of the numbers one through nine exactly once <strong>to</strong> fill in the blacks <strong>and</strong> complete this<br />
equation.<br />
����� − ���� = 33333<br />
The Emperor<br />
You are the ruler of a medieval empire <strong>and</strong> you are about <strong>to</strong> have a celebration <strong>to</strong>morrow. The<br />
celebration is the most important party you have ever hosted. You’ve got 1000 bottles of wine you<br />
were planning <strong>to</strong> open for the celebration, but you find out that one of them is poisoned.<br />
The poison exhibits no symp<strong>to</strong>ms until death. Death occurs within ten <strong>to</strong> twenty hours after<br />
consuming even the minutest amount of poison.<br />
You have over a thous<strong>and</strong> slaves at your disposal <strong>and</strong> just under 24 hours <strong>to</strong> determine which<br />
single bottle is poisoned.<br />
You have a h<strong>and</strong>ful of prisoners about <strong>to</strong> be executed, <strong>and</strong> it would mar your celebration <strong>to</strong><br />
have anyone else killed.<br />
What is the smallest number of prisoners you must have <strong>to</strong> drink from the bottles <strong>to</strong> be absolutely<br />
sure <strong>to</strong> find the poisoned bottle within 24 hours?<br />
The Card Trick<br />
I ask Alex <strong>to</strong> pick any 5 cards out of a deck with no Jokers.<br />
He can inspect then shuffle the deck before picking any five cards. He picks out 5 cards then<br />
h<strong>and</strong>s them <strong>to</strong> me (Peter can’t see any of this). I look at the cards <strong>and</strong> I pick 1 card out <strong>and</strong> give<br />
it back <strong>to</strong> Alex. I then arrange the other four cards in a special way, <strong>and</strong> give those 4 cards all face<br />
down, <strong>and</strong> in a neat pile, <strong>to</strong> Peter.<br />
Peter looks at the 4 cards i gave him, <strong>and</strong> says out loud which card Alex is holding (suit <strong>and</strong><br />
number). How?<br />
The solution uses pure logic, not sleight of h<strong>and</strong>. All Peter needs <strong>to</strong> know is the order of the<br />
cards <strong>and</strong> what is on their face, nothing more.<br />
4.9 Campus Maps / Cartes du <strong>campus</strong><br />
See next page
4.9. CAMPUS MAPS / CARTES DU CAMPUS 81
82 CHAPTER 4. GENERAL INFORMATION / INFORMATIONS GÉNÉRALES
4.9. CAMPUS MAPS / CARTES DU CAMPUS 83